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.

[pre-talk at 1:20pm]