p-adic periods of admissible pairs

Abstract: In this talk, we study a Tannakian category of admissible pairs, which arise naturally when one is comparing etale and de Rham cohomology of p-adic formal schemes. Admissible pairs are parameterized by local Shimura varieties and their non-minuscule generalizations, which admit period mappings to de Rham affine Grassmannians. After reviewing this theory, we will state a result characterizing the basic admissible pairs that admit CM in terms of transcendence of their periods. This result can be seen as a p-adic analogue of a theorem of Cohen and Shiga-Wolfhart characterizing CM abelian varieties in terms of transcendence of their periods. All work is joint with Sean Howe.

number theory

Audience: researchers in the topic

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.