Reductions of Galois representations of slope 3/2

Abstract

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of GQp of slope 32 and exceptional weights. This, along with previous works, completes the description of the reduction for all slopes less than 2. The proof involves computing the reductions of the Banach spaces attached by the p-adic Local Langlands Correspondence (LLC) to these representations, followed by an application of the mod p LLC to recover the reductions of these representations.