LEADER 04251nam 2200793 u 450 001 9910820288703321 005 20230617021736.0 010 $a1-383-02466-9 010 $a1-299-13293-6 010 $a0-19-166372-7 024 7 $a10.1093/oso/9780198528319.001.0001 035 $a(CKB)2670000000331117 035 $a(EBL)1141977 035 $a(OCoLC)830162676 035 $a(SSID)ssj0000907535 035 $a(PQKBManifestationID)11470709 035 $a(PQKBTitleCode)TC0000907535 035 $a(PQKBWorkID)10884489 035 $a(PQKB)11252060 035 $a(Au-PeEL)EBL1141977 035 $a(CaPaEBR)ebr10655433 035 $a(CaONFJC)MIL444543 035 $a(Au-PeEL)EBL4700348 035 $a(OCoLC)960758491 035 $a(Au-PeEL)EBL7038970 035 $a(MiAaPQ)EBC1141977 035 $a(OCoLC)1406787691 035 $a(StDuBDS)9781383024661 035 $a(EXLCZ)992670000000331117 100 $a20040408e20232003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to algebraic geometry and algebraic groups /$fMeinolf Geck$b[electronic resource] 210 1$aOxford :$cOxford University Press,$d2023. 215 $a1 online resource (320 p.) 225 1 $aOxford graduate texts in mathematics ;$v10. 225 1 $aOxford science publications 225 1 $aOxford scholarship online 225 0$aOxford graduate texts in mathematics ;$v10 300 $aFormerly CIP.$5Uk 300 $aPreviously issued in print: 2003. 311 $a0-19-852831-0 311 $a0-19-967616-X 320 $aIncludes bibliographical references (pages [298]-303) and index. 327 $aCover; 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 327 $a2.3 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 327 $a4 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 330 8 $aAn accessible text introducing algebraic geometry and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic geometries from basic principles. 410 0$aOxford graduate texts in mathematics ;$v10. 410 0$aOxford science publications. 410 0$aOxford scholarship online. 606 $aGeometry, Algebraic 606 $aLinear algebraic groups 615 0$aGeometry, Algebraic. 615 0$aLinear algebraic groups. 676 $a516.35 676 $a516.3/5 700 $aGeck$b Meinolf$01710917 801 0$bStDuBDS 801 2$bUk 801 2$bStDuBDSZ 801 2$bStDuBDSZ 906 $aBOOK 912 $a9910820288703321 996 $aAn introduction to algebraic geometry and algebraic groups$94101868 997 $aUNINA