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An introduction to algebraic geometry and algebraic groups / / Meinolf Geck [[electronic resource]]
| An introduction to algebraic geometry and algebraic groups / / Meinolf Geck [[electronic resource]] |
| Autore | Geck Meinolf |
| Pubbl/distr/stampa | Oxford : , : Oxford University Press, , 2023 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina |
516.35
516.3/5 |
| Collana |
Oxford graduate texts in mathematics
Oxford science publications Oxford scholarship online |
| Soggetto topico |
Geometry, Algebraic
Linear algebraic groups |
| ISBN |
1-383-02466-9
1-299-13293-6 0-19-166372-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; 1 Algebraic sets and algebraic groups; 1.1 The Zariski topology on affine space; 1.2 Groebner bases and the Hilbert polynomial; 1.3 Regular maps, direct products, and algebraic groups; 1.4 The tangent space and non-singular points; 1.5 The Lie algebra of a linear algebraic group; 1.6 Groups with a split BN-pair; 1.7 BN-pairs in symplectic and orthogonal groups; 1.8 Bibliographic remarks and exercises; 2 Affine varieties and finite morphisms; 2.1 Hilbert's nullstellensatz and abstract affine varieties; 2.2 Finite morphisms and Chevalley's theorem
2.3 Birational equivalences and normal varieties2.4 Linearization and generation of algebraic groups; 2.5 Group actions on affine varieties; 2.6 The unipotent variety of the special linear groups; 2.7 Bibliographic remarks and exercises; 3 Algebraic representations and Borel subgroups; 3.1 Algebraic representations, solvable groups, and tori; 3.2 The main theorem of elimination theory; 3.3 Grassmannian varieties and flag varieties; 3.4 Parabolic subgroups and Borel subgroups; 3.5 On the structure of Borel subgroups; 3.6 Bibliographic remarks and exercises 4 Frobenius maps and finite groups of Lie type4.1 Frobenius maps and rational structures; 4.2 Frobenius maps and BN-pairs; 4.3 Further applications of the Lang-Steinberg theorem; 4.4 Counting points on varieties over finite fields; 4.5 The virtual characters of Deligne and Lusztig; 4.6 An example: the characters of the Suzuki groups; 4.7 Bibliographic remarks and exercises; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; U; V; W; Z |
| Record Nr. | UNINA-9910820288703321 |
Geck Meinolf
|
||
| Oxford : , : Oxford University Press, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to algebraic geometry and algebraic groups [[electronic resource] /] / Meinolf Geck
| An introduction to algebraic geometry and algebraic groups [[electronic resource] /] / Meinolf Geck |
| Autore | Geck Meinolf |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2003 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina |
516.35
516.3/5 |
| Collana |
Oxford Graduate Texts in Mathematics
Oxford graduate texts in mathematics |
| Soggetto topico |
Geometry, Algebraic
Linear algebraic groups |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-13293-6
0-19-166372-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; 1 Algebraic sets and algebraic groups; 1.1 The Zariski topology on affine space; 1.2 Groebner bases and the Hilbert polynomial; 1.3 Regular maps, direct products, and algebraic groups; 1.4 The tangent space and non-singular points; 1.5 The Lie algebra of a linear algebraic group; 1.6 Groups with a split BN-pair; 1.7 BN-pairs in symplectic and orthogonal groups; 1.8 Bibliographic remarks and exercises; 2 Affine varieties and finite morphisms; 2.1 Hilbert's nullstellensatz and abstract affine varieties; 2.2 Finite morphisms and Chevalley's theorem
2.3 Birational equivalences and normal varieties2.4 Linearization and generation of algebraic groups; 2.5 Group actions on affine varieties; 2.6 The unipotent variety of the special linear groups; 2.7 Bibliographic remarks and exercises; 3 Algebraic representations and Borel subgroups; 3.1 Algebraic representations, solvable groups, and tori; 3.2 The main theorem of elimination theory; 3.3 Grassmannian varieties and flag varieties; 3.4 Parabolic subgroups and Borel subgroups; 3.5 On the structure of Borel subgroups; 3.6 Bibliographic remarks and exercises 4 Frobenius maps and finite groups of Lie type4.1 Frobenius maps and rational structures; 4.2 Frobenius maps and BN-pairs; 4.3 Further applications of the Lang-Steinberg theorem; 4.4 Counting points on varieties over finite fields; 4.5 The virtual characters of Deligne and Lusztig; 4.6 An example: the characters of the Suzuki groups; 4.7 Bibliographic remarks and exercises; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; U; V; W; Z |
| Record Nr. | UNINA-9910463026503321 |
|
Geck Meinolf
|
||
| Oxford ; ; New York, : Oxford University Press, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to algebraic geometry and algebraic groups [[electronic resource] /] / Meinolf Geck
| An introduction to algebraic geometry and algebraic groups [[electronic resource] /] / Meinolf Geck |
| Autore | Geck Meinolf |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2003 |
| Descrizione fisica | 1 online resource (320 p.) |
| Disciplina |
516.35
516.3/5 |
| Collana |
Oxford Graduate Texts in Mathematics
Oxford graduate texts in mathematics |
| Soggetto topico |
Geometry, Algebraic
Linear algebraic groups |
| ISBN |
1-383-02466-9
1-299-13293-6 0-19-166372-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; 1 Algebraic sets and algebraic groups; 1.1 The Zariski topology on affine space; 1.2 Groebner bases and the Hilbert polynomial; 1.3 Regular maps, direct products, and algebraic groups; 1.4 The tangent space and non-singular points; 1.5 The Lie algebra of a linear algebraic group; 1.6 Groups with a split BN-pair; 1.7 BN-pairs in symplectic and orthogonal groups; 1.8 Bibliographic remarks and exercises; 2 Affine varieties and finite morphisms; 2.1 Hilbert's nullstellensatz and abstract affine varieties; 2.2 Finite morphisms and Chevalley's theorem
2.3 Birational equivalences and normal varieties2.4 Linearization and generation of algebraic groups; 2.5 Group actions on affine varieties; 2.6 The unipotent variety of the special linear groups; 2.7 Bibliographic remarks and exercises; 3 Algebraic representations and Borel subgroups; 3.1 Algebraic representations, solvable groups, and tori; 3.2 The main theorem of elimination theory; 3.3 Grassmannian varieties and flag varieties; 3.4 Parabolic subgroups and Borel subgroups; 3.5 On the structure of Borel subgroups; 3.6 Bibliographic remarks and exercises 4 Frobenius maps and finite groups of Lie type4.1 Frobenius maps and rational structures; 4.2 Frobenius maps and BN-pairs; 4.3 Further applications of the Lang-Steinberg theorem; 4.4 Counting points on varieties over finite fields; 4.5 The virtual characters of Deligne and Lusztig; 4.6 An example: the characters of the Suzuki groups; 4.7 Bibliographic remarks and exercises; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; U; V; W; Z |
| Record Nr. | UNINA-9910786146003321 |
|
Geck Meinolf
|
||
| Oxford ; ; New York, : Oxford University Press, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An invitation to quantum cohomology : Kontsevich's formula for rational plane curves / Joachim Kock, Israel Vainsencher
| An invitation to quantum cohomology : Kontsevich's formula for rational plane curves / Joachim Kock, Israel Vainsencher |
| Autore | Kock, Joachim |
| Pubbl/distr/stampa | Boston : Birkhäuser, c2007 |
| Descrizione fisica | xii, 159 p. : ill. ; 24 cm |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | Vainsencher, Israelauthor |
| Collana |
Progress in mathematics (Boston, Mass.) ; v. 249
Progress in mathematics ; vol. 249 |
| Soggetto topico |
Geometry, Enumerative
Quantum theory Homology theory Curves, Plane |
| ISBN |
0817644563
9780817644567 |
| Classificazione |
LC QA607
510.10/510.18 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002418929707536 |
|
Kock, Joachim
|
||
| Boston : Birkhäuser, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""0.1. Selmer sheaves and Kolyvagin systems""; ""0.2. Resemblance to the leading term of an L-function""; ""0.3. Applications""; ""0.4. Layout of the paper""; ""0.5. Notation""; ""0.6. Acknowledgments""; ""Chapter 1. Local Cohomology Groups""; ""1.1. Local conditions""; ""1.2. The finite/singular homomorphism""; ""1.3. Local duality""; ""Chapter 2. Global Cohomology Groups and Selmer Structures""; ""2.1. Selmer modules""; ""2.2. Comparing Selmer modules""; ""2.3. Global duality""; ""Chapter 3. Kolyvagin Systems""; ""3.1. Kolyvagin systems""
""3.2. Euler systems and Kolyvagin systems""""3.3. Simplicial sheaves and Selmer groups""; ""3.4. Sheaves and monodromy""; ""3.5. Hypotheses on T,F, and p""; ""3.6. Choosing useful primes""; ""3.7. Some remarks about hypothesis ( H.6)""; ""Chapter 4. Kolyvagin Systems over Principal Artinian Rings""; ""4.1. The core Selmer module""; ""4.2. Kolyvagin systems and the core rank""; ""4.3. The sheaf of stub Selmer modules""; ""4.4. Kolyvagin systems and the stub Selmer sheaf""; ""4.5. Kolyvagin systems over principal artinian rings""; ""Chapter 5. Kolyvagin Systems over Integral Domains"" ""5.1. Kolyvagin systems over a field""""5.2. Kolyvagin systems over a discrete valuation ring""; ""5.3. Kolyvagin systems over A""; ""Chapter 6. Examples""; ""6.1. The multiplicative group""; ""6.2. Elliptic curves""; ""6.3. The multiplicative group, revisited""; ""Appendix A. Proof of Theorem 3.2.4""; ""Appendix B. Proof of Theorem 4.3.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910478885603321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""0.1. Selmer sheaves and Kolyvagin systems""; ""0.2. Resemblance to the leading term of an L-function""; ""0.3. Applications""; ""0.4. Layout of the paper""; ""0.5. Notation""; ""0.6. Acknowledgments""; ""Chapter 1. Local Cohomology Groups""; ""1.1. Local conditions""; ""1.2. The finite/singular homomorphism""; ""1.3. Local duality""; ""Chapter 2. Global Cohomology Groups and Selmer Structures""; ""2.1. Selmer modules""; ""2.2. Comparing Selmer modules""; ""2.3. Global duality""; ""Chapter 3. Kolyvagin Systems""; ""3.1. Kolyvagin systems""
""3.2. Euler systems and Kolyvagin systems""""3.3. Simplicial sheaves and Selmer groups""; ""3.4. Sheaves and monodromy""; ""3.5. Hypotheses on T,F, and p""; ""3.6. Choosing useful primes""; ""3.7. Some remarks about hypothesis ( H.6)""; ""Chapter 4. Kolyvagin Systems over Principal Artinian Rings""; ""4.1. The core Selmer module""; ""4.2. Kolyvagin systems and the core rank""; ""4.3. The sheaf of stub Selmer modules""; ""4.4. Kolyvagin systems and the stub Selmer sheaf""; ""4.5. Kolyvagin systems over principal artinian rings""; ""Chapter 5. Kolyvagin Systems over Integral Domains"" ""5.1. Kolyvagin systems over a field""""5.2. Kolyvagin systems over a discrete valuation ring""; ""5.3. Kolyvagin systems over A""; ""Chapter 6. Examples""; ""6.1. The multiplicative group""; ""6.2. Elliptic curves""; ""6.3. The multiplicative group, revisited""; ""Appendix A. Proof of Theorem 3.2.4""; ""Appendix B. Proof of Theorem 4.3.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910788746203321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Kolyvagin systems / / Barry Mazur, Karl Rubin
| Kolyvagin systems / / Barry Mazur, Karl Rubin |
| Autore | Mazur Barry |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2004 |
| Descrizione fisica | 1 online resource (112 p.) |
| Disciplina | 516.3/5 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Birch-Swinnerton-Dyer conjecture
L-functions Arithmetical algebraic geometry |
| ISBN | 1-4704-0397-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Introduction""; ""0.1. Selmer sheaves and Kolyvagin systems""; ""0.2. Resemblance to the leading term of an L-function""; ""0.3. Applications""; ""0.4. Layout of the paper""; ""0.5. Notation""; ""0.6. Acknowledgments""; ""Chapter 1. Local Cohomology Groups""; ""1.1. Local conditions""; ""1.2. The finite/singular homomorphism""; ""1.3. Local duality""; ""Chapter 2. Global Cohomology Groups and Selmer Structures""; ""2.1. Selmer modules""; ""2.2. Comparing Selmer modules""; ""2.3. Global duality""; ""Chapter 3. Kolyvagin Systems""; ""3.1. Kolyvagin systems""
""3.2. Euler systems and Kolyvagin systems""""3.3. Simplicial sheaves and Selmer groups""; ""3.4. Sheaves and monodromy""; ""3.5. Hypotheses on T,F, and p""; ""3.6. Choosing useful primes""; ""3.7. Some remarks about hypothesis ( H.6)""; ""Chapter 4. Kolyvagin Systems over Principal Artinian Rings""; ""4.1. The core Selmer module""; ""4.2. Kolyvagin systems and the core rank""; ""4.3. The sheaf of stub Selmer modules""; ""4.4. Kolyvagin systems and the stub Selmer sheaf""; ""4.5. Kolyvagin systems over principal artinian rings""; ""Chapter 5. Kolyvagin Systems over Integral Domains"" ""5.1. Kolyvagin systems over a field""""5.2. Kolyvagin systems over a discrete valuation ring""; ""5.3. Kolyvagin systems over A""; ""Chapter 6. Examples""; ""6.1. The multiplicative group""; ""6.2. Elliptic curves""; ""6.3. The multiplicative group, revisited""; ""Appendix A. Proof of Theorem 3.2.4""; ""Appendix B. Proof of Theorem 4.3.3""; ""Bibliography"" |
| Record Nr. | UNINA-9910813658303321 |
|
Mazur Barry
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures in real geometry [[electronic resource] /] / editor Fabrizio Broglia
| Lectures in real geometry [[electronic resource] /] / editor Fabrizio Broglia |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1996 |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | BrogliaFabrizio <1948-> |
| Collana | De Gruyter Expositions in Mathematics |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-081111-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Foreword -- Introduction -- Table of Contents -- Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals / Roy, Marie-Françoise -- Nash functions and manifolds / Shiota, Masahiro -- Approximation theorems in real analytic and algebraic geometry / Tognoli, A. -- Real abelian varieties and real algebraic curves / Ciliberto, Ciro / Pedrini, Claudio -- Mario Raimondo's contributions to real geometry / Tognoli, Alberto -- Mario Raimondo's contributions to computer algebra / Recio, Tomas / Alonso, Maria-Emilia |
| Record Nr. | UNINA-9910462480303321 |
| Berlin ; ; New York, : Walter de Gruyter, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures in real geometry [[electronic resource] /] / editor Fabrizio Broglia
| Lectures in real geometry [[electronic resource] /] / editor Fabrizio Broglia |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1996 |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | BrogliaFabrizio <1948-> |
| Collana | De Gruyter Expositions in Mathematics |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| ISBN | 3-11-081111-1 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Foreword -- Introduction -- Table of Contents -- Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals / Roy, Marie-Françoise -- Nash functions and manifolds / Shiota, Masahiro -- Approximation theorems in real analytic and algebraic geometry / Tognoli, A. -- Real abelian varieties and real algebraic curves / Ciliberto, Ciro / Pedrini, Claudio -- Mario Raimondo's contributions to real geometry / Tognoli, Alberto -- Mario Raimondo's contributions to computer algebra / Recio, Tomas / Alonso, Maria-Emilia |
| Record Nr. | UNINA-9910785522603321 |
| Berlin ; ; New York, : Walter de Gruyter, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures in real geometry / / editor Fabrizio Broglia
| Lectures in real geometry / / editor Fabrizio Broglia |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1996 |
| Descrizione fisica | 1 online resource (282 p.) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | BrogliaFabrizio <1948-> |
| Collana | De Gruyter Expositions in Mathematics |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| ISBN | 3-11-081111-1 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Foreword -- Introduction -- Table of Contents -- Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of reals / Roy, Marie-Françoise -- Nash functions and manifolds / Shiota, Masahiro -- Approximation theorems in real analytic and algebraic geometry / Tognoli, A. -- Real abelian varieties and real algebraic curves / Ciliberto, Ciro / Pedrini, Claudio -- Mario Raimondo's contributions to real geometry / Tognoli, Alberto -- Mario Raimondo's contributions to computer algebra / Recio, Tomas / Alonso, Maria-Emilia |
| Record Nr. | UNINA-9910816185503321 |
| Berlin ; ; New York, : Walter de Gruyter, 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
