Cohomological degree-shifting operators on Shimura varieties

Abstract: An automorphic form can appear in multiple degrees of the cohomology of arithmetic manifolds, and this happens mostly when the arithmetic manifolds are not algebraic. This phenomenon is a part of the "derived" structures of the Langlands program, suggested by Venkatesh. However, even over algebraic arithmetic manifolds, certain automorphic forms like weight-one elliptic modular forms possess a derived structure. In this talk, we discuss this idea over Shimura varieties. A part of the story is the construction of archimedean/p-adic "derived" operators on the cohomology of Shimura varieties, using complex/p-adic Hodge theory.

number theory

Audience: researchers in the topic

Harvard number theory seminar