Geodesic
Reductions of Galois representations for slopes in $(1,2)$
Documenta mathematica, Tome 20 (2015), pp. 943-987.

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

Summary: We describe the semisimplifications of the mod $p$ reductions of certain crystalline two-dimensional local Galois representations of slopes in $(1,2)$ and all weights. The proof uses the compatibility between the $p$-adic and mod $p$ Local Langlands Correspondences for $\{GL}_2(\Q_p)$. We also give a complete description of the submodules generated by the second highest monomial in the mod $p$ symmetric power representations of ${\{GL}}_2(\F_p)$.
Classification : 11F80
Keywords: reductions of Galois representations, local Langlands correspondence, Hecke operators 
@article{DOCMA_2015__20__a14,
     author = {Bhattacharya, Shalini and Ghate, Eknath},
     title = {Reductions of {Galois} representations for slopes in $(1,2)$},
     journal = {Documenta mathematica},
     pages = {943--987},
     publisher = {mathdoc},
     volume = {20},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a14/}
}
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Bhattacharya, Shalini; Ghate, Eknath. Reductions of Galois representations for slopes in $(1,2)$. Documenta mathematica, Tome 20 (2015), pp. 943-987. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a14/