Geometric extensions

Abstract

The complex points of an algebraic variety has a rich topological structure, and many results in the smooth situation may be extended to the singular case by working with intersection cohomology in the constructible derived category of sheaves. In this talk I'll define the geometric extension E(X) of a singular algebraic variety X, a formally defined object that recovers intersection cohomology over the rationals and parity sheaves in the mod p schubert variety setting. This construction also gives a definition of (p completed) intersection K theory, and a real mod two version of intersection cohomology, answering an old question of Goresky-Macpherson.

There will be an expository talk from 1-2pm on: What is a sheaf?