An introduction to algebraic geometry and algebraic groups
- United Kingdom Oxford University Press 2003
- xii,307p.
Introduces algebraic geometries and algebraic groups by developing the language of algebraic geometry from scratch and using it to set up the theory of affine algebraic groups from first principles. 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. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.