Shrenik Shah (Columbia University)
Some strong twisted base changes for unitary similitude groups

Building upon the work of Morel and Labesse, Skinner and Shin associate to certain cohomological cuspidal automorphic representations on a unitary similitude group a base change to G_m x GL_n such that the expected local-global compatibility relations hold at places where either the unitary group is split or the representation and group are both unramified. In this paper we prove compatibility at odd places where the group is ramified quasi-split and the representation is spherical for a certain special maximal compact subgroup. This allows us to unconditionally construct many strong twisted base changes for unitary similitude groups, which are needed, for instance, in work of Skinner-Urban on the Bloch-Kato conjecture. We obtain new cases of the generalized Ramanujan conjecture in this setting. The proof uses the doubling method, the local theory of p-adic representations, variation in p-adic families, and p-adic analytic contination of periods.