Seminar

Title: Reductions mod p of semi-stable representations.

Abstract:

We describe a new method to compute the reductions mod p of irreducible two-dimensional semi-stable representations of the absolute Galois group \GQp of \Qp. This method uses the compatibility with respect to reduction mod p between the p-adic Local Langlands Correspondence and the Iwahori theoretic version of the mod p Local Langlands Correspondence. By estimating certain logarithmic functions on \Qp by polynomials on open subsets of \Zp, we compute the reductions mod p completely for weights at most p + 1. We also state how this method can be used, in theory, to compute the reductions mod p of semi-stable representations of arbitrarily large weights.

This talk is based on a joint work with Eknath Ghate.

For details, please refer to https://arxiv.org/abs/2311.03740