[Lissité générique pour les anneaux de déformations potentiellement semi-stables à valeurs dans ]
Nous étendons les résultats de Kisin sur la structure des anneaux de déformations de représentations galoisiennes en caractéristique aux anneaux de déformations de représentations galoisiennes à valeurs dans des groupes connexes reductifs . En particulier, nous prouvons que ces anneaux de déformations de représentations galoisiennes sont d’intersection complète. De plus, nous étudions la structure de l’espace de modules des -modules (cadrés) quand . Nous prouvons que a une composante irréductible singulière quand , et nous construisons une résolution des singularités avec interprétation modulaire.
We extend Kisin’s results on the structure of characteristic Galois deformation rings to deformation rings of Galois representations valued in arbitrary connected reductive groups . In particular, we show that such Galois deformation rings are complete intersections. In addition, we study explicitly the structure of the moduli space of (framed) -modules when . We show that when and , has a singular irreducible component, and we construct a moduli-theoretic resolution of singularities.
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Keywords: $p$-adic Hodge theory, deformation rings, algebraic groups
Mot clés : théorie d’Hodge $p$-adique, anneaux de déformations, groupes algébrique
@article{AIF_2016__66_6_2565_0,
author = {Bellovin, Rebecca},
title = {Generic smoothness for $G$-valued potentially semi-stable deformation rings},
journal = {Annales de l'Institut Fourier},
pages = {2565--2620},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {6},
year = {2016},
doi = {10.5802/aif.3072},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3072/}
}
TY - JOUR AU - Bellovin, Rebecca TI - Generic smoothness for $G$-valued potentially semi-stable deformation rings JO - Annales de l'Institut Fourier PY - 2016 SP - 2565 EP - 2620 VL - 66 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3072/ DO - 10.5802/aif.3072 LA - en ID - AIF_2016__66_6_2565_0 ER -
%0 Journal Article %A Bellovin, Rebecca %T Generic smoothness for $G$-valued potentially semi-stable deformation rings %J Annales de l'Institut Fourier %D 2016 %P 2565-2620 %V 66 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3072/ %R 10.5802/aif.3072 %G en %F AIF_2016__66_6_2565_0
Bellovin, Rebecca. Generic smoothness for $G$-valued potentially semi-stable deformation rings. Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2565-2620. doi : 10.5802/aif.3072. http://www.numdam.org/articles/10.5802/aif.3072/
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