Finiteness Theorems for Deformations of Complexes
[Théorèmes de finitude pour déformations de complexes]
Bleher, Frauke M.1 ; Chinburg, Ted2
1 University of Iowa Department of Mathematics Iowa City, IA 52242-1419 (U.S.A.)
2 University of Pennsylvania Department of Mathematics Philadelphia, PA 19104-6395 (U.S.A.)
Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 573-612.

Nous considérons les déformations de complexes bornés de G-modules, sur un corps de caractéristique positive lorsque G est un groupe profini. Nous démontrons un théorème de finitude qui fournit des conditions suffisantes pour que la déformation verselle d’un tel complexe puisse être représentée par un complexe de G-modules strictement parfait sur l’anneau de déformation verselle associé.

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of G-modules that is strictly perfect over the associated versal deformation ring.

DOI : 10.5802/aif.2770
Classification : 11F80, 20E18, 18E30
Keywords: Versal and universal deformations, derived categories, finiteness questions, tame fundamental groups
Mot clés : déformations verselles et universelles, catégories dérivées, questions de finitude, groupes fondamentaux modérés
Bleher, Frauke M. 1 ; Chinburg, Ted 2

1 University of Iowa Department of Mathematics Iowa City, IA 52242-1419 (U.S.A.)
2 University of Pennsylvania Department of Mathematics Philadelphia, PA 19104-6395 (U.S.A.) 
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Bleher, Frauke M.; Chinburg, Ted. Finiteness Theorems for Deformations of Complexes. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 573-612. doi : 10.5802/aif.2770. http://www.numdam.org/articles/10.5802/aif.2770/

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