Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors
| Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1994] |
| Descrizione fisica | 1 online resource (ix, 220 p. ) |
| Disciplina | 512/.74 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Algebraic number theory
Geometry, Algebraic Iwasawa theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-7765-8
0-8218-5511-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910480560703321 |
| Providence, Rhode Island : , : American Mathematical Society, , [1994] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors
| Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1994] |
| Descrizione fisica | 1 online resource (ix, 220 p. ) |
| Disciplina | 512/.74 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Algebraic number theory
Geometry, Algebraic Iwasawa theory |
| ISBN |
0-8218-7765-8
0-8218-5511-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910788644803321 |
| Providence, Rhode Island : , : American Mathematical Society, , [1994] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors
| Arithmetic geometry : Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, March 15-18, 1993, Arizona State University / / Nancy Childress, John W. Jones, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1994] |
| Descrizione fisica | 1 online resource (ix, 220 p. ) |
| Disciplina | 512/.74 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Algebraic number theory
Geometry, Algebraic Iwasawa theory |
| ISBN |
0-8218-7765-8
0-8218-5511-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910827541303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [1994] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hilbert modular forms and Iwasawa theory [[electronic resource] /] / Haruzo Hida
| Hilbert modular forms and Iwasawa theory [[electronic resource] /] / Haruzo Hida |
| Autore | Hida Haruzo |
| Pubbl/distr/stampa | Oxford, : Clarendon, 2006 |
| Descrizione fisica | 1 online resource (417 p.) |
| Disciplina | 512.74 |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
Forms, Modular
Hilbert modular surfaces Iwasawa theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-90406-2
9786610904068 0-19-151387-3 1-4294-6994-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 1 Introduction; 1.1 Classical Iwasawa theory; 1.1.1 Galois theoretic interpretation of the class group; 1.1.2 The Iwasawa algebra as a deformation ring; 1.1.3 Pseudo-representations; 1.1.4 Two-dimensional universal deformations; 1.2 Selmer groups; 1.2.1 Deligne's rationality conjecture; 1.2.2 Ordinary Galois representations; 1.2.3 Greenberg's Selmer groups; 1.2.4 Selmer groups with general coefficients; 1.3 Deformation and adjoint square Selmer groups; 1.3.1 Nearly ordinary deformation rings; 1.3.2 Adjoint square Selmer groups and differentials
1.3.3 Universal deformation rings are noetherian1.3.4 Elliptic modularity at a glance; 1.4 Iwasawa theory for deformation rings; 1.4.1 Galois action on deformation rings; 1.4.2 Control of adjoint square Selmer groups; 1.4.3 Λ-adic forms; 1.5 Adjoint square L-invariants; 1.5.1 Balanced Selmer groups; 1.5.2 Greenberg's L-invariant; 1.5.3 Proof of Theorem 1.80; 2 Automorphic forms on inner forms of GL(2); 2.1 Quaternion algebras over a number field; 2.1.1 Quaternion algebras; 2.1.2 Orders of quaternion algebras; 2.2 A short review of algebraic geometry; 2.2.1 Affine schemes 2.2.2 Affine algebraic groups2.2.3 Schemes; 2.3 Automorphic forms on quaternion algebras; 2.3.1 Arithmetic quotients; 2.3.2 Archimedean Hilbert modular forms; 2.3.3 Hilbert modular forms with integral coefficients; 2.3.4 Duality and Hecke algebras; 2.3.5 Quaternionic automorphic forms; 2.3.6 The Jacquet-Langlands correspondence; 2.3.7 Local representations of GL(2); 2.3.8 Modular Galois representations; 2.4 The integral Jacquet-Langlands correspondence; 2.4.1 Classical Hecke operators; 2.4.2 Hecke algebras; 2.4.3 Cohomological correspondences; 2.4.4 Eichler-Shimura isomorphisms 2.5 Theta series2.5.1 Quaternionic theta series; 2.5.2 Siegel's theta series; 2.5.3 Transformation formulas; 2.5.4 Theta series of imaginary quadratic fields; 2.6 The basis problem of Eichler; 2.6.1 The elliptic Jacquet-Langlands correspondence; 2.6.2 Eichler's integral correspondence; 3 Hecke algebras as Galois deformation rings; 3.1 Hecke algebras; 3.1.1 Automorphic forms on definite quaternions; 3.1.2 Hecke operators; 3.1.3 Inner products; 3.1.4 Ordinary Hecke algebras; 3.1.5 Automorphic forms of higher weight; 3.2 Galois deformation; 3.2.1 Minimal deformation problems 3.2.2 Tangent spaces of local deformation functors3.2.3 Taylor-Wiles systems; 3.2.4 Hecke algebras are universal; 3.2.5 Flat deformations; 3.2.6 Freeness over the Hecke algebra; 3.2.7 Hilbert modular basis problems; 3.2.8 Locally cyclotomic deformation; 3.2.9 Locally cyclotomic Hecke algebras; 3.2.10 Global deformation over a p-adic field; 3.3 Base change; 3.3.1 p-Ordinary Jacquet-Langlands correspondence; 3.3.2 Base fields of odd degree; 3.3.3 Automorphic base change; 3.3.4 Galois base change; 3.4 L-invariants of Hilbert modular forms; 3.4.1 Statement of the result 3.4.2 Deformation without monodromy conditions |
| Record Nr. | UNINA-9910465635803321 |
Hida Haruzo
|
||
| Oxford, : Clarendon, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hilbert modular forms and Iwasawa theory [[electronic resource] /] / Haruzo Hida
| Hilbert modular forms and Iwasawa theory [[electronic resource] /] / Haruzo Hida |
| Autore | Hida Haruzo |
| Pubbl/distr/stampa | Oxford, : Clarendon, 2006 |
| Descrizione fisica | 1 online resource (417 p.) |
| Disciplina | 512.74 |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
Forms, Modular
Hilbert modular surfaces Iwasawa theory |
| ISBN |
1-280-90406-2
9786610904068 0-19-151387-3 1-4294-6994-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 1 Introduction; 1.1 Classical Iwasawa theory; 1.1.1 Galois theoretic interpretation of the class group; 1.1.2 The Iwasawa algebra as a deformation ring; 1.1.3 Pseudo-representations; 1.1.4 Two-dimensional universal deformations; 1.2 Selmer groups; 1.2.1 Deligne's rationality conjecture; 1.2.2 Ordinary Galois representations; 1.2.3 Greenberg's Selmer groups; 1.2.4 Selmer groups with general coefficients; 1.3 Deformation and adjoint square Selmer groups; 1.3.1 Nearly ordinary deformation rings; 1.3.2 Adjoint square Selmer groups and differentials
1.3.3 Universal deformation rings are noetherian1.3.4 Elliptic modularity at a glance; 1.4 Iwasawa theory for deformation rings; 1.4.1 Galois action on deformation rings; 1.4.2 Control of adjoint square Selmer groups; 1.4.3 Λ-adic forms; 1.5 Adjoint square L-invariants; 1.5.1 Balanced Selmer groups; 1.5.2 Greenberg's L-invariant; 1.5.3 Proof of Theorem 1.80; 2 Automorphic forms on inner forms of GL(2); 2.1 Quaternion algebras over a number field; 2.1.1 Quaternion algebras; 2.1.2 Orders of quaternion algebras; 2.2 A short review of algebraic geometry; 2.2.1 Affine schemes 2.2.2 Affine algebraic groups2.2.3 Schemes; 2.3 Automorphic forms on quaternion algebras; 2.3.1 Arithmetic quotients; 2.3.2 Archimedean Hilbert modular forms; 2.3.3 Hilbert modular forms with integral coefficients; 2.3.4 Duality and Hecke algebras; 2.3.5 Quaternionic automorphic forms; 2.3.6 The Jacquet-Langlands correspondence; 2.3.7 Local representations of GL(2); 2.3.8 Modular Galois representations; 2.4 The integral Jacquet-Langlands correspondence; 2.4.1 Classical Hecke operators; 2.4.2 Hecke algebras; 2.4.3 Cohomological correspondences; 2.4.4 Eichler-Shimura isomorphisms 2.5 Theta series2.5.1 Quaternionic theta series; 2.5.2 Siegel's theta series; 2.5.3 Transformation formulas; 2.5.4 Theta series of imaginary quadratic fields; 2.6 The basis problem of Eichler; 2.6.1 The elliptic Jacquet-Langlands correspondence; 2.6.2 Eichler's integral correspondence; 3 Hecke algebras as Galois deformation rings; 3.1 Hecke algebras; 3.1.1 Automorphic forms on definite quaternions; 3.1.2 Hecke operators; 3.1.3 Inner products; 3.1.4 Ordinary Hecke algebras; 3.1.5 Automorphic forms of higher weight; 3.2 Galois deformation; 3.2.1 Minimal deformation problems 3.2.2 Tangent spaces of local deformation functors3.2.3 Taylor-Wiles systems; 3.2.4 Hecke algebras are universal; 3.2.5 Flat deformations; 3.2.6 Freeness over the Hecke algebra; 3.2.7 Hilbert modular basis problems; 3.2.8 Locally cyclotomic deformation; 3.2.9 Locally cyclotomic Hecke algebras; 3.2.10 Global deformation over a p-adic field; 3.3 Base change; 3.3.1 p-Ordinary Jacquet-Langlands correspondence; 3.3.2 Base fields of odd degree; 3.3.3 Automorphic base change; 3.3.4 Galois base change; 3.4 L-invariants of Hilbert modular forms; 3.4.1 Statement of the result 3.4.2 Deformation without monodromy conditions |
| Record Nr. | UNINA-9910792233803321 |
|
Hida Haruzo
|
||
| Oxford, : Clarendon, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hilbert modular forms and Iwasawa theory / / Haruzo Hida
| Hilbert modular forms and Iwasawa theory / / Haruzo Hida |
| Autore | Hida Haruzo |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford, : Clarendon, 2006 |
| Descrizione fisica | 1 online resource (417 p.) |
| Disciplina | 512.74 |
| Collana | Oxford mathematical monographs |
| Soggetto topico |
Forms, Modular
Hilbert modular surfaces Iwasawa theory |
| ISBN |
1-280-90406-2
9786610904068 0-19-151387-3 1-4294-6994-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 1 Introduction; 1.1 Classical Iwasawa theory; 1.1.1 Galois theoretic interpretation of the class group; 1.1.2 The Iwasawa algebra as a deformation ring; 1.1.3 Pseudo-representations; 1.1.4 Two-dimensional universal deformations; 1.2 Selmer groups; 1.2.1 Deligne's rationality conjecture; 1.2.2 Ordinary Galois representations; 1.2.3 Greenberg's Selmer groups; 1.2.4 Selmer groups with general coefficients; 1.3 Deformation and adjoint square Selmer groups; 1.3.1 Nearly ordinary deformation rings; 1.3.2 Adjoint square Selmer groups and differentials
1.3.3 Universal deformation rings are noetherian1.3.4 Elliptic modularity at a glance; 1.4 Iwasawa theory for deformation rings; 1.4.1 Galois action on deformation rings; 1.4.2 Control of adjoint square Selmer groups; 1.4.3 Λ-adic forms; 1.5 Adjoint square L-invariants; 1.5.1 Balanced Selmer groups; 1.5.2 Greenberg's L-invariant; 1.5.3 Proof of Theorem 1.80; 2 Automorphic forms on inner forms of GL(2); 2.1 Quaternion algebras over a number field; 2.1.1 Quaternion algebras; 2.1.2 Orders of quaternion algebras; 2.2 A short review of algebraic geometry; 2.2.1 Affine schemes 2.2.2 Affine algebraic groups2.2.3 Schemes; 2.3 Automorphic forms on quaternion algebras; 2.3.1 Arithmetic quotients; 2.3.2 Archimedean Hilbert modular forms; 2.3.3 Hilbert modular forms with integral coefficients; 2.3.4 Duality and Hecke algebras; 2.3.5 Quaternionic automorphic forms; 2.3.6 The Jacquet-Langlands correspondence; 2.3.7 Local representations of GL(2); 2.3.8 Modular Galois representations; 2.4 The integral Jacquet-Langlands correspondence; 2.4.1 Classical Hecke operators; 2.4.2 Hecke algebras; 2.4.3 Cohomological correspondences; 2.4.4 Eichler-Shimura isomorphisms 2.5 Theta series2.5.1 Quaternionic theta series; 2.5.2 Siegel's theta series; 2.5.3 Transformation formulas; 2.5.4 Theta series of imaginary quadratic fields; 2.6 The basis problem of Eichler; 2.6.1 The elliptic Jacquet-Langlands correspondence; 2.6.2 Eichler's integral correspondence; 3 Hecke algebras as Galois deformation rings; 3.1 Hecke algebras; 3.1.1 Automorphic forms on definite quaternions; 3.1.2 Hecke operators; 3.1.3 Inner products; 3.1.4 Ordinary Hecke algebras; 3.1.5 Automorphic forms of higher weight; 3.2 Galois deformation; 3.2.1 Minimal deformation problems 3.2.2 Tangent spaces of local deformation functors3.2.3 Taylor-Wiles systems; 3.2.4 Hecke algebras are universal; 3.2.5 Flat deformations; 3.2.6 Freeness over the Hecke algebra; 3.2.7 Hilbert modular basis problems; 3.2.8 Locally cyclotomic deformation; 3.2.9 Locally cyclotomic Hecke algebras; 3.2.10 Global deformation over a p-adic field; 3.3 Base change; 3.3.1 p-Ordinary Jacquet-Langlands correspondence; 3.3.2 Base fields of odd degree; 3.3.3 Automorphic base change; 3.3.4 Galois base change; 3.4 L-invariants of Hilbert modular forms; 3.4.1 Statement of the result 3.4.2 Deformation without monodromy conditions |
| Record Nr. | UNINA-9910819649703321 |
|
Hida Haruzo
|
||
| Oxford, : Clarendon, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hilbert modular forms and Iwasawa theory / Haruzo Hida
| Hilbert modular forms and Iwasawa theory / Haruzo Hida |
| Autore | Hida, Haruzo |
| Pubbl/distr/stampa | Oxford : Clarendon, c2006 |
| Descrizione fisica | xiv, 402 p. ill. ; 24 cm |
| Disciplina | 512.74 |
| Collana |
Oxford mathematical monographs
Oxford science publications |
| Soggetto topico |
Forms, Modular
Hilbert modular surfaces Iwasawa theory |
| ISBN | 019857102X |
| Classificazione |
AMS 11F41
AMS 11-02 AMS 11R23 LC QA243.H42 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001983829707536 |
|
Hida, Haruzo
|
||
| Oxford : Clarendon, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg
| Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg |
| Autore | Greenberg Ralph <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Curves, Elliptic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0609-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction.""; ""1.1. Congruence relations.""; ""1.2. Selmer groups for elliptic curves.""; ""1.3. Behavior of Iwasawa invariants.""; ""1.4. Selmer atoms.""; ""1.5. Parity questions.""; ""1.6. Other situations.""; ""1.7. Organization and acknowledgements.""; ""Chapter 2. Projective and quasi-projective modules.""; ""2.1. Criteria for projectivity and quasi-projectivity.""; ""2.2. Nonzero -invariant.""; ""2.3. The structure of G/to.G .""; ""2.4. Projective dimension.""; ""Chapter 3. Projectivity or quasi-projectivity of XE0(K).""
""3.1. The proof of Theorem 1.""""3.2. Quasi-projectivity.""; ""3.3. Partial converses.""; ""3.4. More general situations.""; ""3.5. -extensions.""; ""Chapter 4. Selmer atoms.""; ""4.1. Various cohomology groups. Coranks. Criteria for vanishing.""; ""4.2. Selmer groups for E[p].""; ""4.3. Justification of (1.4.b) and (1.4.c).""; ""4.4. Justification of (1.4.d) and the proof of Theorem 2.""; ""4.5. Finiteness of Selmer atoms.""; ""Chapter 5. The structure of Hv(K, E).""; ""5.1. Determination of E,v().""; ""5.2. Determination of ""426830A E,v, ""526930B ."" ""5.3. Projectivity and Herbrand quotients.""""Chapter 6. The case where is a p-group.""; ""Chapter 7. Other specific groups.""; ""7.1. The groups A4, S4, and S5.""; ""7.2. The group PGL2(Fp).""; ""7.3. The groups PGL2(Z/pr+1Z) for r 1.""; ""7.4. Extensions of (Z/pZ) by a p-group.""; ""Chapter 8. Some arithmetic illustrations.""; ""8.1. An illustration where 0 is empty.""; ""8.2. An illustration where 0 is non-empty.""; ""8.3. An illustration where the ""0365ss's have abelian image.""; ""8.4. False Tate extensions of Q.""; ""Chapter 9. Self-dual representations."" ""9.1. Various classes of groups.""""9.2. groups.""; ""9.3. Some parity results concerning multiplicities.""; ""9.4. Self-dual representations and the decomposition map.""; ""Chapter 10. A duality theorem.""; ""10.1. The main result.""; ""10.2. Consequences concerning the parity of sE().""; ""Chapter 11. p-modular functions.""; ""11.1. Basic examples of p-modular functions.""; ""11.2. Some p-modular functions involving multiplicities.""; ""Chapter 12. Parity.""; ""12.1. The proof of Theorem 3.""; ""12.2. Consequences concerning WDel(E,) and WSelp(E,)."" ""Chapter 13. More arithmetic illustrations.""""13.1. An illustration where E K/F is empty.""; ""13.2. An illustration where K Q(E[p]).""; ""13.3. An illustration where Gal(K/Q) is isomorphic to Bn or Hn.""; ""Bibliography"" |
| Record Nr. | UNINA-9910479861803321 |
|
Greenberg Ralph <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg
| Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg |
| Autore | Greenberg Ralph <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Curves, Elliptic |
| ISBN | 1-4704-0609-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction.""; ""1.1. Congruence relations.""; ""1.2. Selmer groups for elliptic curves.""; ""1.3. Behavior of Iwasawa invariants.""; ""1.4. Selmer atoms.""; ""1.5. Parity questions.""; ""1.6. Other situations.""; ""1.7. Organization and acknowledgements.""; ""Chapter 2. Projective and quasi-projective modules.""; ""2.1. Criteria for projectivity and quasi-projectivity.""; ""2.2. Nonzero -invariant.""; ""2.3. The structure of G/to.G .""; ""2.4. Projective dimension.""; ""Chapter 3. Projectivity or quasi-projectivity of XE0(K).""
""3.1. The proof of Theorem 1.""""3.2. Quasi-projectivity.""; ""3.3. Partial converses.""; ""3.4. More general situations.""; ""3.5. -extensions.""; ""Chapter 4. Selmer atoms.""; ""4.1. Various cohomology groups. Coranks. Criteria for vanishing.""; ""4.2. Selmer groups for E[p].""; ""4.3. Justification of (1.4.b) and (1.4.c).""; ""4.4. Justification of (1.4.d) and the proof of Theorem 2.""; ""4.5. Finiteness of Selmer atoms.""; ""Chapter 5. The structure of Hv(K, E).""; ""5.1. Determination of E,v().""; ""5.2. Determination of ""426830A E,v, ""526930B ."" ""5.3. Projectivity and Herbrand quotients.""""Chapter 6. The case where is a p-group.""; ""Chapter 7. Other specific groups.""; ""7.1. The groups A4, S4, and S5.""; ""7.2. The group PGL2(Fp).""; ""7.3. The groups PGL2(Z/pr+1Z) for r 1.""; ""7.4. Extensions of (Z/pZ) by a p-group.""; ""Chapter 8. Some arithmetic illustrations.""; ""8.1. An illustration where 0 is empty.""; ""8.2. An illustration where 0 is non-empty.""; ""8.3. An illustration where the ""0365ss's have abelian image.""; ""8.4. False Tate extensions of Q.""; ""Chapter 9. Self-dual representations."" ""9.1. Various classes of groups.""""9.2. groups.""; ""9.3. Some parity results concerning multiplicities.""; ""9.4. Self-dual representations and the decomposition map.""; ""Chapter 10. A duality theorem.""; ""10.1. The main result.""; ""10.2. Consequences concerning the parity of sE().""; ""Chapter 11. p-modular functions.""; ""11.1. Basic examples of p-modular functions.""; ""11.2. Some p-modular functions involving multiplicities.""; ""Chapter 12. Parity.""; ""12.1. The proof of Theorem 3.""; ""12.2. Consequences concerning WDel(E,) and WSelp(E,)."" ""Chapter 13. More arithmetic illustrations.""""13.1. An illustration where E K/F is empty.""; ""13.2. An illustration where K Q(E[p]).""; ""13.3. An illustration where Gal(K/Q) is isomorphic to Bn or Hn.""; ""Bibliography"" |
| Record Nr. | UNINA-9910788866003321 |
|
Greenberg Ralph <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg
| Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg |
| Autore | Greenberg Ralph <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (185 p.) |
| Disciplina | 512.7/4 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Iwasawa theory
Curves, Elliptic |
| ISBN | 1-4704-0609-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Chapter 1. Introduction.""; ""1.1. Congruence relations.""; ""1.2. Selmer groups for elliptic curves.""; ""1.3. Behavior of Iwasawa invariants.""; ""1.4. Selmer atoms.""; ""1.5. Parity questions.""; ""1.6. Other situations.""; ""1.7. Organization and acknowledgements.""; ""Chapter 2. Projective and quasi-projective modules.""; ""2.1. Criteria for projectivity and quasi-projectivity.""; ""2.2. Nonzero -invariant.""; ""2.3. The structure of G/to.G .""; ""2.4. Projective dimension.""; ""Chapter 3. Projectivity or quasi-projectivity of XE0(K).""
""3.1. The proof of Theorem 1.""""3.2. Quasi-projectivity.""; ""3.3. Partial converses.""; ""3.4. More general situations.""; ""3.5. -extensions.""; ""Chapter 4. Selmer atoms.""; ""4.1. Various cohomology groups. Coranks. Criteria for vanishing.""; ""4.2. Selmer groups for E[p].""; ""4.3. Justification of (1.4.b) and (1.4.c).""; ""4.4. Justification of (1.4.d) and the proof of Theorem 2.""; ""4.5. Finiteness of Selmer atoms.""; ""Chapter 5. The structure of Hv(K, E).""; ""5.1. Determination of E,v().""; ""5.2. Determination of ""426830A E,v, ""526930B ."" ""5.3. Projectivity and Herbrand quotients.""""Chapter 6. The case where is a p-group.""; ""Chapter 7. Other specific groups.""; ""7.1. The groups A4, S4, and S5.""; ""7.2. The group PGL2(Fp).""; ""7.3. The groups PGL2(Z/pr+1Z) for r 1.""; ""7.4. Extensions of (Z/pZ) by a p-group.""; ""Chapter 8. Some arithmetic illustrations.""; ""8.1. An illustration where 0 is empty.""; ""8.2. An illustration where 0 is non-empty.""; ""8.3. An illustration where the ""0365ss's have abelian image.""; ""8.4. False Tate extensions of Q.""; ""Chapter 9. Self-dual representations."" ""9.1. Various classes of groups.""""9.2. groups.""; ""9.3. Some parity results concerning multiplicities.""; ""9.4. Self-dual representations and the decomposition map.""; ""Chapter 10. A duality theorem.""; ""10.1. The main result.""; ""10.2. Consequences concerning the parity of sE().""; ""Chapter 11. p-modular functions.""; ""11.1. Basic examples of p-modular functions.""; ""11.2. Some p-modular functions involving multiplicities.""; ""Chapter 12. Parity.""; ""12.1. The proof of Theorem 3.""; ""12.2. Consequences concerning WDel(E,) and WSelp(E,)."" ""Chapter 13. More arithmetic illustrations.""""13.1. An illustration where E K/F is empty.""; ""13.2. An illustration where K Q(E[p]).""; ""13.3. An illustration where Gal(K/Q) is isomorphic to Bn or Hn.""; ""Bibliography"" |
| Record Nr. | UNINA-9910827648203321 |
|
Greenberg Ralph <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
