TuTh 3:00-4:00PM or by appointment in 423 Thackeray.
Math 3550: The course is an introduction to linear algebraic groups with an emphasis on the structure and classification of semisimple algebraic groups over an algebraically closed field. Highlights of the course include theorems of Borel, Chevalley, Grothendieck, Kolchin, Tannaka, Tits.
Math 3501: The course is a continuation of Math 3550 Lie Theory: Affine Algebraic Groups. A first goal is to complete the treatment of the structure and classification of reductive affine algebraic groups over an algebraically closed field. A second goal is to discuss the theory of affine group schemes of finite type over a field (not necessarily algebraically closed).
Math 3550: Some basic familiarity with ring theory and category theory. Some background in classical algebraic geometry at introductory graduate level would be helpful.
Math 3501: Math 3550.
A. Borel, Linear Algebraic Groups. In: Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math. IX), 1966.
A. Borel, Linear Algebraic Groups. 2nd edition. GTM 126, Springer 1991.
J. Humphreys, Linear Algebraic Groups. GTM 21, Springer 1975.
T. Springer, Linear Algebraic Groups. 2nd edition. Progress in Mathematics 9, Birkhäuser 1998.
A. Kleshchev, Lectures on Algebraic Groups.
W. Waterhouse, Introduction to Affine Group Schemes. GTM 66, Springer 1979.
J. Milne, Algebraic Groups. Cambridge Studies in Advanced Mathematics 170, Cambridge, 2017.
Group schemes (SGA 3). Vol. I-III. Séminaire de Géométrie Algébrique du Bois Marie 1962-64.
Algebraic Groups and Discontinuous Subgroups. Proc. Sympos. Pure Math. IX), AMS, Providence, RI, 1966.
B. Conrad, A modern proof of Chevalley's theorem on algebraic groups.
J. Ramanujan Math. Soc. 17 (2002), no. 1, 1-18.
The final grade will be computed from the following:
| Homework: | 50% | |
| Final Project: | 50% |
Homework 1.Due Wednesday, November 18:
Homework 2.Due TBD:
Homework 3.