Title: Descent and Cohomological Descent
Speaker: Prof Nitin Nitsure, TIFR, Mumbai
Date: 23 August 2013
Time: 3:00 - 4:00 p.m.
Venue: Lecture Hall I, Department of Mathematics
Around 1960, Grothendieck developed the theory of descent. The aim of this theory is to construct geometric objects on a base space – in particular bundles, sheaves and their sections – in terms a generalized covering space which is visualized to lie
upstairs' over the base space. The objects over the base space are obtained by descending’ similar objects from the covering space. In late 1960s-early 1970s, Deligne addressed the problem of how to understand cohomology of the base space via cohomology of a covering, by this time descending cohomology classes (instead of just descending global sections of sheaves, which is the case of 0th cohomology). The theory developed by Deligne, known as `Cohomological Descent’ has found important applications to Hodge theory and to cohomology of algebraic stacks. In these two expository lectures, I will begin with a quick look at Grothendieck’s theory of descent, and then go on to give a brief introduction to Deligne’s theory of Cohomological Descent.