Przemyslaw Chojecki (University of Oxford)
Companion points on definite unitary eigenvarieties

Abstract: We study companion points on the eigenvariety associated to a unitary group G compact at infinity. We deduce some cases of Breuil's conjecture on the locally analytic socle and relate it to Hansen's conjecture. In particular we prove that certain locally analytic principal series inject into locally analytic vectors of the completed cohomology of G. This is a joint work with John Bergdall.