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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 | ||
| ||