Finiteness Theorems for Deformations of Complexes

Bleher, Frauke M.; Chinburg, Ted

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.

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

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