We prove the existence of local constancy phenomena for reductions in a general (odd) prime power setting of two-dimensional irreducible crystalline representations of
Nous prouvons l’existence du phénomène de constance locale pour les réductions modulo
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Mots-clés : Integral p-adic Hodge Theory, Crystalline Representations,
Emiliano Torti 1

@article{JTNB_2022__34_2_345_0, author = {Emiliano Torti}, title = {Local constancy for reductions of two-dimensional crystalline representations}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {345--370}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {34}, number = {2}, year = {2022}, doi = {10.5802/jtnb.1205}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1205/} }
TY - JOUR AU - Emiliano Torti TI - Local constancy for reductions of two-dimensional crystalline representations JO - Journal de théorie des nombres de Bordeaux PY - 2022 SP - 345 EP - 370 VL - 34 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1205/ DO - 10.5802/jtnb.1205 LA - en ID - JTNB_2022__34_2_345_0 ER -
%0 Journal Article %A Emiliano Torti %T Local constancy for reductions of two-dimensional crystalline representations %J Journal de théorie des nombres de Bordeaux %D 2022 %P 345-370 %V 34 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1205/ %R 10.5802/jtnb.1205 %G en %F JTNB_2022__34_2_345_0
Emiliano Torti. Local constancy for reductions of two-dimensional crystalline representations. Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 2, pp. 345-370. doi : 10.5802/jtnb.1205. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1205/
[1] Limiting measures of supersingularities (2021) (https://arxiv.org/abs/1991.12220)
[2] On the reductions of certain two-dimensional crystalline representations, III (2021) (https://arxiv.org/abs/2102.13568)
[3] Ranks of Selmer groups in an analytic family, Trans. Am. Math. Soc., Volume 364 (2012) no. 9, pp. 4735-4761 | DOI | MR | Zbl
[4]
[5] Reductions of Some Two-Dimensional Crystalline Representations via Kisin Modules, Int. Math. Res. Not., Volume 2022 (2022) no. 4, pp. 3170-3197 | DOI | MR | Zbl
[6] Limites de représentations cristallines, Compos. Math., Volume 140 (2004) no. 6, pp. 1473-1498 | DOI | Zbl
[7] Trianguline representations, Bull. Lond. Math. Soc., Volume 43 (2011) no. 4, pp. 619-635 | DOI | MR | Zbl
[8] Local constancy for the reduction
[9] Familles de représentations de de Rham et monodromie
[10] Construction of some families of 2-dimensional crystalline representations, Math. Ann., Volume 329 (2004) no. 2, pp. 365-377 | DOI | MR | Zbl
[11] Reduction of certain crystalline representations and local constancy in the weight space (2018) (https://arxiv.org/abs/1801.07754)
[12] Reductions of Galois representations for slopes in
[13] Reductions of Galois representations of slope 1, J. Algebra, Volume 508 (2018), pp. 98-156 | DOI | MR | Zbl
[14] Non-Archimedean analysis, Grundlehren der Mathematischen Wissenschaften, 261, Springer, 1984, xii+436 pages | DOI
[15] Elements of mathematics. Algebra I. Chapters 1–3, Springer, 1998
[16] Sur quelques représentations modulaires et
[17] Explicit reduction modulo
[18] Sur la densité des représentations cristallines de
[19] Une application des variétés de Hecke des groupes unitaires, Shimura varieties (London Mathematical Society Lecture Note Series), Volume 457, Cambridge University Press, 2020, pp. 266-296 | Zbl
[20] On the semi-simplicity of the
[21] Représentations triangulines de dimension 2, Représentation
[22]
[23] Construction des représentations
[24] Several approaches to non-Archimedean geometry,
[25]
[26] Représentations
[27] A zig-zag conjecture and local constancy for Galois representations (2019) (https://arxiv.org/abs/1903.08996)
[28]
[29] A
[30] Deformations of
[31] On some crystalline representations of
[32] On the locus of
[33] Motives for modular forms, Invent. Math., Volume 100 (1990) no. 2, pp. 419-430 | DOI | MR | Zbl
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