LEADER 04226nam 2200685 a 450 001 9910463026503321 005 20211005094149.0 010 $a1-299-13293-6 010 $a0-19-166372-7 035 $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(MiAaPQ)EBC1141977 035 $a(Au-PeEL)EBL1141977 035 $a(CaPaEBR)ebr10655433 035 $a(CaONFJC)MIL444543 035 $a(MiAaPQ)EBC4700348 035 $a(Au-PeEL)EBL4700348 035 $a(OCoLC)960758491 035 $a(EXLCZ)992670000000331117 100 $a20040408d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to algebraic geometry and algebraic groups$b[electronic resource] /$fMeinolf Geck 210 $aOxford ;$aNew York $cOxford University Press$d2003 215 $a1 online resource (320 p.) 225 1 $aOxford Graduate Texts in Mathematics ;$vv.10 225 0$aOxford graduate texts in mathematics ;$v10 300 $aFirst published in paperback 2013. 311 $a0-19-852831-0 311 $a0-19-967616-X 320 $aIncludes bibliographical references (p. [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 $aAn accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups 410 0$aOxford Graduate Texts in Mathematics 606 $aGeometry, Algebraic 606 $aLinear algebraic groups 608 $aElectronic books. 615 0$aGeometry, Algebraic. 615 0$aLinear algebraic groups. 676 $a516.35 676 $a516.3/5 700 $aGeck$b Meinolf$01046979 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910463026503321 996 $aAn introduction to algebraic geometry and algebraic groups$92474291 997 $aUNINA