Date: Friday, February 02, 2018
Location: 1096 East Hall (3:10 PM to 4:10 PM)
Title: Chern classes of automorphic vector bundles (note special day, time, place)
Abstract: Holomorphic modular forms on the Shimura variety S(G) attached to the reductive group G can be interpreted naturally as sections of automorphic vector bundles: locally free sheaves that can be defined analytically by exploiting the structure of a Shimura variety as a quotient of a symmetric space. The construction can also be made algebraic, and in this way one gets a canonical functor from the tensor category of representations of a certain Levi subgroup K of G to the tensor category of vector bundles on S(G), and thus a homomorphism from the representation ring of K to K_0(S(G)). When S(G) is compact we determine how the image of this homomorphism behaves under Chern characters to Deligne cohomology and continuous ladic cohomology. When S(G) is noncompact and of abelian type, we use perfectoid geometry to define Chern classes in the ladic cohomology of the minimal compactification of S(G); these are analogous to the topological cohomology classes defined by Goresky and Pardon, using differential geometry. (Joint work with Helene Esnault.)
Files:
Speaker: Michael Harris
Institution: Columbia University
Event Organizer: Kartik Prasanna
