Course on Geometric Satake isomorphism, spring 2014
Course on Geometric Satake isomorphism, spring 2014
Lecturer
Scope
5 sp.
Type
Advanced studies
Prerequisites
Basic algebra.
Description
This course aims to give an introduction to the geometric Satake isomorphism, which
is a first instance of geometric Langlands duality. The tentative topics of the course will
include the following:
- Basic introduction to affine algebraic groups, root datum, Borel subgroups, flag variety
- Structure properties of reductive algebraic groups
- Tannakian formalism, recovering a group from its representations
- Introduction to derived categories, perverse sheaves
- Affine Grassmannian
- Geometric Satake isomorphism
The topics might vary depending on the interest of the audience.
Lectures
Weeks 3-9, Tuesday 12-14 and Friday 14-16 in room B321
Requirements
Weekly homework
Exercise Set 1
Exercise Set 2
Exercise Set 3
Exercise Set 4
Bibliography
Mirković, I.; Vilonen, K. Geometric Langlands duality and representations of algebraic groups over commutative rings. Ann. of Math. (2) 166 (2007), no. 1, 95–143.
Borel, A. Linear algebraic groups. Second edition. Graduate Texts in Mathematics, 126. Springer-Verlag, New York, 1991.
Humphreys, J. E. Linear algebraic groups. Graduate Texts in Mathematics, No. 21. Springer-Verlag, New York-Heidelberg, 1975.
Springer, T. A. Linear algebraic groups. Second edition. Progress in Mathematics, 9. Birkhäuser Boston, Inc., Boston, MA, 1998.
Milne, J.S. Basic theory of affine group schemes. .
Conrad, B. Reductive group schemes. http://math.stanford.edu/~conrad/papers/luminysga3.pdf.
Waterhouse, William C. Introduction to affine group schemes. Graduate Texts in Mathematics, 66. Springer-Verlag, New York-Berlin, 1979.
Deligne, P; Milne, J.S.; Ogus, A.; Shih, K. Hodge cycles, motives, and Shimura varieties. Lecture Notes in Mathematics, 900. Springer-Verlag, Berlin-New York, 1982.
Registration
Did you forget to register? What to do?