Induction and restriction in formal deformation of coverings

doi:https://doi.org/10.48550/arxiv.math/0205228

Open AccessPreprint10.48550/arxiv.math/0205228

Induction and restriction in formal deformation of coverings

José Bertin,Ariane Mézard-2002-05-22-arXiv (Cornell University)

TL;DRAbstract

Let X/S be a semistable curve with an action of a finite group G and let H be a normal subgroup of G. We present a new condition under which for any base change T->S, (X/G)*T is isomorphic to (X*T)/G. This allows us to define induction and restriction morphisms between the G-equivariant deformation functor of X and the G/H-equivariant (resp. H-equivariant) deformation functor of X/H (resp. X).

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Let X/S be a semistable curve with an action of a finite group G and let H be a normal subgroup of G. We present a new condition under which for any base change T->S, (X/G)*T is isomorphic to (X*T)/G. This allows us to define induction and restriction morphisms between the G-equivariant deformation functor of X and the G/H-equivariant (resp. H-equivariant) deformation functor of X/H (resp. X).

Keywords

FunctorEquivariant mapMathematicsMorphismPure mathematicsBase (topology)Base changeAction (physics)

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