An Introduction to Algebraic Geometry and Algebraic Groups: 10 (Oxford Graduate Texts in Mathematics) - Hardcover

Geck, Meinolf

Hardcover

ISBN 10: 0198528310 ISBN 13: 9780198528319

Publisher: OUP Oxford, 2003

Synopsis

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.

About this title

Review

'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.' (EMS Newsletter)

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 Professor in Pure Mathematics at the Institute of Mathematics, King's College, University of Aberdeen

Edition details

• Publisher: OUP Oxford
• Publication date: 2003
• ISBN 10: 0198528310
• ISBN 13: 9780198528319
• Binding: Hardcover
• Language: English
• Number of pages: 320