Number Theory: Cohomological degree-shifting operators on Shimura varieties


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November 9, 2022 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Gyujin Oh - Columbia

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.