An 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 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 and Lie type. The text covers the conjugacy of borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions, and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new proofs. The text uses algebraic groups as the main examples, including worked out examples, instructuve exercises, as well as bibliographical and historical remarks.
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The style of exposition in the book is very reader-friendly ... The proofs are clear and complete. Mathematical Reviews
About the Author
Meinolf Geck is at Institut Girard Desargues, Universite Lyon.
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In this first chapter, we introduce the basic objects: algebraic sets in affine space, the corresponding affine algebras, and algebraic groups. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
connected affine algebraic group, closed connected solvable subgroup, affine quotient, infinite perfect field, upper unitriangular matrices, unipotent variety, unipotent classes, affine algebraic groups, irreducible affine varieties, closed connected subgroup, irreducible algebraic set, map cpx, closed irreducible subset, unipotent elements, finite morphism, irreducible affine variety, noetherian topological space, dominant morphism, invertible diagonal matrices, algebraic sets, constructible subset, monomial order, linear algebraic group, differential criterion, semisimple elements Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Let, Proof Let, Lemma Let, Proposition Let, Example Let, Definition Let, Proof First, Theorem Let, Corollary Let, Remark Let, Example Assume, Exercise Assume, Lemma Assume, Proof Assume, Proof By Corollary New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this first chapter, we introduce the basic objects: algebraic sets in affine space, the corresponding affine algebras, and algebraic groups. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
connected affine algebraic group, closed connected solvable subgroup, affine quotient, infinite perfect field, upper unitriangular matrices, unipotent variety, unipotent classes, affine algebraic groups, irreducible affine varieties, closed connected subgroup, irreducible algebraic set, map cpx, closed irreducible subset, unipotent elements, finite morphism, irreducible affine variety, noetherian topological space, dominant morphism, invertible diagonal matrices, algebraic sets, constructible subset, monomial order, linear algebraic group, differential criterion, semisimple elements Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Let, Proof Let, Lemma Let, Proposition Let, Example Let, Definition Let, Proof First, Theorem Let, Corollary Let, Remark Let, Example Assume, Exercise Assume, Lemma Assume, Proof Assume, Proof By Corollary New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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