Seminar Event Detail

Group, Lie and Number Theory

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 l-adic cohomology. When S(G) is non-compact and of abelian type, we use perfectoid geometry to define Chern classes in the l-adic 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.)


Speaker:  Michael Harris
Institution:  Columbia University

Event Organizer:   Kartik Prasanna   


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