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.