04251nam 2200793 u 450 991082028870332120230617021736.01-383-02466-91-299-13293-60-19-166372-710.1093/oso/9780198528319.001.0001(CKB)2670000000331117(EBL)1141977(OCoLC)830162676(SSID)ssj0000907535(PQKBManifestationID)11470709(PQKBTitleCode)TC0000907535(PQKBWorkID)10884489(PQKB)11252060(Au-PeEL)EBL1141977(CaPaEBR)ebr10655433(CaONFJC)MIL444543(Au-PeEL)EBL4700348(OCoLC)960758491(Au-PeEL)EBL7038970(MiAaPQ)EBC1141977(OCoLC)1406787691(StDuBDS)9781383024661(EXLCZ)99267000000033111720040408e20232003 uy 0engur|n|---|||||txtccrAn introduction to algebraic geometry and algebraic groups /Meinolf Geck[electronic resource]Oxford :Oxford University Press,2023.1 online resource (320 p.)Oxford graduate texts in mathematics ;10.Oxford science publicationsOxford scholarship onlineOxford graduate texts in mathematics ;10Formerly CIP.UkPreviously issued in print: 2003.0-19-852831-0 0-19-967616-X Includes bibliographical references (pages [298]-303) and index.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 theorem2.3 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 exercises4 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; ZAn accessible text introducing algebraic geometry and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic geometries from basic principles.Oxford graduate texts in mathematics ;10.Oxford science publications.Oxford scholarship online.Geometry, AlgebraicLinear algebraic groupsGeometry, Algebraic.Linear algebraic groups.516.35516.3/5Geck Meinolf1710917StDuBDSUkStDuBDSZStDuBDSZBOOK9910820288703321An introduction to algebraic geometry and algebraic groups4101868UNINA