Eknath Ghate (TIFR and IAS)
Reductions of Galois representations of small slopes

Abstract: We use the compatibility between the p-adic and mod p Local Langlands Correspondences to compute the reductions of certain crystalline representations of the local Galois group of Q_p. The reduction is now essentially completely known for all slopes smaller than 2, thanks to joint work with Shalini Bhattacharaya, and also with Sandra Rozensztajn for the case of slope 1. We shall speak about these works, contrasting the behavior of the reduction in the fractional and integral slope cases.