Multiplicity-one for p-adic automorphic cohomology

Abstract: Automorphic representations give rise to classes in the p-adic cohomology of locally symmetric spaces. In the setting of GL_n over a CM field, the contribution of a given representation is spread across several cohomological degrees. A conjecture of Venkatesh (together with a relevant case of the Bloch--Kato conjecture) explains this phenomenon in a precise way in terms of the Galois representation attached to the automorphic representation. In this talk, I will introduce this conjecture and describe how it may be viewed as a multiplicity-one statement suggested by a general conjecture within the Langlands program. Then, I will present recent results establishing Venkatesh's conjecture under various technical assumptions (and in the p-adic setting).

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

KIAS HCMC Algebra Seminar

Series comments: This list only contains virtual talks hosted by HCMC Algebra Seminar. For in-person talks, please visit the seminar webpage.