Algebraic Geometry Seminar

The Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber is a

massive generalization of certain theorems in Hodge theory. It is a powerful tool for

studying the cohomology, with coefficients in a field of characteristic

zero, of complex algebraic varieties.  For applications to modular representation

theory, it would be highly desirable to have an analog of the Decomposition Theorem that

applies to the cohomology of complex algebraic varieties with coefficients

in fields of characteristic p>0.  In this talk, I will give a brief introduction to the

Decomposition Theorem and discuss joint work with D. Juteau and G.

Williamson, in which we provide a weak analog of the Decomposition Theorem, applicable to

various examples of interest in modular representation theory.