Geodesic
On the reductions of certain two-dimensional crystalline representations
Documenta mathematica, Tome 26 (2021), pp. 1929-1979.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The question of computing the reductions modulo $p$ of two-dimensional crystalline $p$-adic Galois representations has been studied extensively, and partial progress has been made for representations that have small weights, very small slopes, or very large slopes. It was conjectured by Breuil, Buzzard, and Emerton that these reductions are irreducible if they have even weight and non-integer slope. We prove some instances of this conjecture for slopes up to $\frac{p-1}{2}$.
Classification : 11S20
Keywords: crystalline, residual, irreducible, Langlands, slopes 
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     author = {Arsovski, Bodan},
     title = {On the reductions of certain two-dimensional crystalline representations},
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Arsovski, Bodan. On the reductions of certain two-dimensional crystalline representations. Documenta mathematica, Tome 26 (2021), pp. 1929-1979. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a3/