[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.
Révisé le :
Accepté le :
Publié le :
Keywords: $p$-adic Hodge theory, deformation rings, algebraic groups
Mot 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, Tome 66 (2016) no. 6, pp. 2565-2620. doi : 10.5802/aif.3072. https://aif.centre-mersenne.org/articles/10.5802/aif.3072/
[1] G-valued potentially semi-stable deformation rings, ProQuest LLC, Ann Arbor, MI, 2012, 71 pages Thesis (Ph.D.)–The University of Chicago
[2] -adic Hodge theory in rigid analytic families, Algebra Number Theory, Volume 9 (2015) no. 2, pp. 371-433 | DOI
[3] Generic fibers of deformation rings (http://math.stanford.edu/~conrad/modseminar/pdf/L04.pdf)
[4] Irreducible components of rigid spaces, Ann. Inst. Fourier (Grenoble), Volume 49 (1999) no. 2, pp. 473-541 | DOI
[5] Reductive group schemes, Proceedings of the SGA3 Summer School (Luminy, Aug.-Sept. 2011), Volume 1 (Panoramas et Synthèses), Societé Mathematique de France, 2014 (To appear. Available at http://www.math.ens.fr/~gille/sem/notes434.html)
[6] Tannakian Categories, Hodge Cycles, Motives, and Shimura Varieties (LNM), Volume 900, Springer, New York, 1982, pp. 101-228
[7] Séminaire de géométrie algébrique du Bois Marie 1962/64; Schémas en groupes, 3, Springer, 1970
[8] The universal family of semi-stable -adic Galois representations (Preprint. http://arxiv.org/abs/1312.6371)
[9] Linear algebraic groups, Springer-Verlag, New York, 1975, xiv+247 pages (Graduate Texts in Mathematics, No. 21)
[10] Conjugacy classes in semisimple algebraic groups, Mathematical Surveys and Monographs, 43, American Mathematical Society, Providence, RI, 1995, xviii+196 pages
[11] Nilpotent orbits in representation theory, Lie theory (Progr. Math.), Volume 228, Birkhäuser Boston, Boston, MA, 2004, pp. 1-211
[12] Potentially semi-stable deformation rings, J. Amer. Math. Soc., Volume 21 (2008) no. 2, pp. 513-546 | DOI
[13] The Fontaine-Mazur conjecture for , J. Amer. Math. Soc., Volume 22 (2009) no. 3, pp. 641-690 | DOI
[14] Moduli of finite flat group schemes and modularity, Ann. of Math. (2), Volume 170 (2009) no. 3, pp. 1085-1180 | DOI
[15] e-mail to Brian Conrad, 2012
[16] Nilpotent subalgebras of semisimple Lie algebras, C. R. Math. Acad. Sci. Paris, Volume 347 (2009) no. 9-10, pp. 477-482 | DOI
[17] Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, Cambridge, 1989, xiv+320 pages (Translated from the Japanese by M. Reid)
[18] An introduction to the deformation theory of Galois representations, Modular forms and Fermat’s last theorem (Boston, MA, 1995), Springer, New York, 1997, pp. 243-311
[19] Nilpotent orbits over ground fields of good characteristic, Math. Ann., Volume 329 (2004) no. 1, pp. 49-85 | DOI
[20] Catégories Tannakiennes, Lecture Notes in Mathematics, Vol. 265, Springer-Verlag, Berlin, 1972, ii+418 pages
[21] Cohomology of Vector Bundles and Syzygies, Cambridge Tracts in Mathematics, 149, Cambridge University Press, Cambridge, 2003, xiv+371 pages | DOI
Cité par Sources :
