An Introduction to Algebraic Geometry and Algebraic Groups
Series: Oxford Graduate Texts in Mathematics; 10;
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Product details:
- Publisher OUP Oxford
- Date of Publication 14 March 2013
- ISBN 9780199676163
- Binding Paperback
- No. of pages320 pages
- Size 233x157x16 mm
- Weight 488 g
- Language English 0
Categories
Short description:
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
MoreLong description:
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.
The author's intention was to write a quick introduction to the area of algebraic groups of the Lie type over fields of positive characteristic and I think he was very successful. The first part of the book can be recommended as a very suitable text for undergraduate students at the beginning of their studies.
Table of Contents:
Algebraic sets and algebraic groups
Affine varieties and finite morphisms
Algebraic representations and Borel subgroups
Frobenius maps and finite groups of Lie type
Bibliography
Index
