By Meinolf Geck
An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first principles.
Building at the historical past fabric from algebraic geometry and algebraic teams, the textual content presents an advent to extra complex and specialized fabric. An instance is the illustration thought of finite teams of Lie type.
The textual content covers the conjugacy of Borel subgroups and maximal tori, the speculation of algebraic teams with a BN-pair, an intensive remedy of Frobenius maps on affine kinds and algebraic teams, zeta services and Lefschetz numbers for forms over finite fields. specialists within the box will take pleasure in a few of the new ways to classical results.
The textual content makes use of algebraic teams because the major examples, together with labored out examples, instructive workouts, in addition to bibliographical and old remarks.
Read Online or Download An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics) PDF
Similar Algebraic Geometry books
The speculation of elliptic curves is distinctive via its lengthy background and through the range of the equipment which have been utilized in its examine. This ebook treats the mathematics process in its smooth formula, by using simple algebraic quantity thought and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal team of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and worldwide fields.
This seriously class-tested ebook is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A uncomplicated wisdom of algebra and topology on the first 12 months graduate point of an American collage is believed. the 1st half is anxious with hyperbolic geometry and discrete teams.
Quantity 2: Schemes and complicated Manifolds, covers generalizations in various instructions of the affine and projective forms that shape the cloth for the 1st quantity. Discusses the origins of algebraic geometry. Paper. DLC: Geometry - Algebraic.
Additional resources for An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics)