Deformation functors of local actions

2011/12/01 by Jakub Byszewski, Byszewski, Jakub
Mathematics · #11G20 #14B12 (Primary) #14D15 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1112.0352

openalex publication_date 2011/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a deformation functor of a local G-action as a smooth extension of a fibered product of functors related to a subgroup and a quotient group of G.

Citations

• Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic

Related

• Deformations and automorphisms: a framework for globalizing local tangent and obstruction spaces
• Cohomology of deformations
• Extended deformation functors
• Deformation theory from the point of view of fibered categories
• The deformation theory of representations of the fundamental group of a smooth variety