EVENT DETAILS AND ABSTRACT

Title: Tate extensions in the cohomology of a Baily-Borel compactification
Speaker: Eduard Looijenga
Speaker Info: Yau Mathematical Sciences Centre, Tsinghua University, Beijing
Brief Description:
Special Note:
Abstract:

An automorphic vector bundle on a Shimura variety will in general not extend to as a bundle to its Baily-Borel compactification. Yet Goresky and Pardon showed that the Chern classes of such a bundle do so in a natural manner. They wondered whether these classes lie in rational cohomology. We show that these extensions have a natural description in the setting of mixed Hodge theory and may not lie in rational cohomology. We apply this to the stable cohomology of the Baily-Borel compactification of the ppav's and show that they yield the basic nontrivial Tate extensions.