Reductions of Crystalline Representations for Small Weights

TL;DR

This paper explicitly computes the reductions of certain crystalline Galois representations with small Hodge-Tate weights, providing detailed results for specific weight ranges.

Contribution

It offers explicit calculations of crystalline representation reductions for small weights, extending understanding in p-adic Hodge theory.

Findings

Explicit reductions for weights in specified ranges

Detailed descriptions of Galois representation behavior

Advances in understanding small weight crystalline representations

Abstract

We compute explicit reductions of crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_{p^f})$ with labeled Hodge-Tate weights in the range $p+2\le k_{0}\le 2p-4$ and $2\le k_i\le p-3$ for $1\le i\le f-1$.