An algorithm for computing the reduction of 2-dimensional crystalline representations of $\text{Gal}(\overline\mathbf{Q}_p/\mathbf{Q}_p)$
Résumé
We describe an algorithm to compute the reduction modulo p of a crystalline Galois representation of dimension 2 of $\text{Gal}(\overline\mathbf{Q}_p/\mathbf{Q}_p)$ with distinct Hodge-Tate weights via the semi-simple modulo p Langlands correspondence. We give some examples computed with an implementation of this algorithm in SAGE.