Number Theory Seminar

I will explain a group theoretic result (joint work with Mark Kisin and Keerthi Madapusi Pera) on Kottwitz isocrystals and Hodge cocharacters for a connected reductive group G over Q_p, which holds under a technical hypothesis on G (which is always satisfied if G is quasi-split and sometimes satisfied if G is not quasi-split). This result implies, under the same hypothesis, that the Newton strata in the mod p fiber of a Hodge-type Shimura variety is non-empty. Rong Zhou also proved a similar result under a different hypothesis by a somewhat different method.