Reductions of modular Galois representations of Slope (2,3)

TL;DR

This paper computes the semisimplifications of mod-p reductions of 2-dimensional crystalline Galois representations with slopes 2 and 3, extending previous work to arbitrary weights.

Contribution

It provides explicit calculations of mod-p reductions for slopes (2,3) in crystalline Galois representations, advancing understanding of their structure.

Findings

Explicit semisimplification formulas for slope 2 and 3 cases

Extension of previous results to arbitrary weights

Enhanced classification of mod-p Galois representations

Abstract

We compute the semisimplifications of the mod-$p$ reductions of $2$-dimensional crystalline representations of the absolute Galois group of the p-adic numbers of slope $(2,3)$ and arbitrary weight, building on work of Bhattacharya-Ghate