Vasudevan Srinivas

Title: On stratified vector bundles in characteristic p

Abstract:

This is a report on some work with Helene Esnault, motivated by a
conjecture of Gieseker, which was proved earlier by Esnault and Mehta.

For a smooth quasi-projective variety $X$ over $\bar{\F}_p$, with trivial
etale $\pi_1$, such that $X$ has a projective normal compactification with
codimension 2 boundary, we show that all stratified vector bundles on $X$
are trivial.

Another result of ours is the following: if a  morphism of smooth
projective varieties in char. p induces the trivial map
on étale fundamental groups, then the pullback of any stratified vector
bundle is trivial, as a stratified bundle.

The talk will discuss these results, along with some background and examples.