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.
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.
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Keywords: $p$-adic Hodge theory, deformation rings, algebraic groups
Mots-clés : théorie d’Hodge $p$-adique, anneaux de déformations, groupes algébrique
Bellovin, Rebecca 1
@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 = {https://aif.centre-mersenne.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 - https://aif.centre-mersenne.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 https://aif.centre-mersenne.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, Volume 66 (2016) no. 6, pp. 2565-2620. doi : 10.5802/aif.3072. https://aif.centre-mersenne.org/articles/10.5802/aif.3072/
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