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Elliptic curves and arithmetic invariants / / Haruzo Hida
| Elliptic curves and arithmetic invariants / / Haruzo Hida |
| Autore | Hida Haruzo |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | New York, : Springer, 2013 |
| Descrizione fisica | 1 online resource (xviii, 449 pages) : illustrations |
| Disciplina | 516.352 |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Number theory
Elliptic functions |
| ISBN | 1-4614-6657-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Non-triviality of Arithmetic Invariants -- 2 Elliptic Curves and Modular Forms -- 3 Invariants, Shimura Variety and Hecke Algebra -- 4 Review of Scheme Theory -- 5 Geometry of Variety -- 6 Elliptic and Modular Curves over Rings.- 7 Modular Curves as Shimura Variety.- 8 Non-vanishing Modulo p of Hecke L–values.- 9 p-Adic Hecke L-functions and their μ-invariants.- 10 Toric Subschemes in a Split Formal Torus -- 11 Hecke Stable Subvariety is a Shimura Subvariety -- References -- Symbol Index -- Statement Index -- Subject Index. |
| Record Nr. | UNINA-9910438135703321 |
Hida Haruzo
|
||
| New York, : Springer, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric modular forms and elliptic curves [[electronic resource] /] / Haruzo Hida
| Geometric modular forms and elliptic curves [[electronic resource] /] / Haruzo Hida |
| Autore | Hida Haruzo |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (468 p.) |
| Disciplina | 516.3/52 |
| Soggetto topico |
Curves, Elliptic
Forms, Modular |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-66971-3
9786613646644 981-4368-65-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Preface to the second edition; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma
1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level 2.9.3 Irreducibility of p-Ordinary Moduli |
| Record Nr. | UNINA-9910451616803321 |
|
Hida Haruzo
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric modular forms and elliptic curves [[electronic resource] /] / Haruzo Hida
| Geometric modular forms and elliptic curves [[electronic resource] /] / Haruzo Hida |
| Autore | Hida Haruzo |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (468 p.) |
| Disciplina | 516.3/52 |
| Soggetto topico |
Curves, Elliptic
Forms, Modular |
| ISBN |
1-280-66971-3
9786613646644 981-4368-65-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Preface to the second edition; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma
1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level 2.9.3 Irreducibility of p-Ordinary Moduli |
| Record Nr. | UNINA-9910779012403321 |
|
Hida Haruzo
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric modular forms and elliptic curves / / Haruzo Hida
| Geometric modular forms and elliptic curves / / Haruzo Hida |
| Autore | Hida Haruzo |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (468 p.) |
| Disciplina | 516.3/52 |
| Soggetto topico |
Curves, Elliptic
Forms, Modular |
| ISBN |
1-280-66971-3
9786613646644 981-4368-65-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Preface to the second edition; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma
1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level 2.9.3 Irreducibility of p-Ordinary Moduli |
| Record Nr. | UNINA-9910823326403321 |
|
Hida Haruzo
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| 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 |
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Hida Haruzo
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| Oxford, : Clarendon, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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