An introduction to algebraic geometry and algebraic groups
著者
書誌事項
An introduction to algebraic geometry and algebraic groups
（Oxford graduate texts in mathematics, 10）
Oxford University Press, 2013
- : pbk
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注記
Includes bibliographical references (p. [298]-303) and index
"First published 2003. First published in paperback 2013"--T.p. verso
"Oxford graduate texts in mathematics 20"--Cover
内容説明・目次
内容説明
An 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 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 approaches to classical results.
The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.
目次
- 1. Algebraic sets and algebraic groups
- 2. Affine varieties and finite morphisms
- 3. Algebraic representations and Borel subgroups
- 4. Frobenius maps and finite groups of Lie type
- Bibliography
- Index
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