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The local lifting problem for actions of finite groups on curves

Ted Chinburg;  Robert Guralnick;  David Harbater — 2011

Annales scientifiques de l'École Normale Supérieure

Let k be an algebraically closed field of characteristic p > 0 . We study obstructions to lifting to characteristic 0 the faithful continuous action φ of a finite group G on k [ [ t ] ] . To each such  φ a theorem of Katz and Gabber associates an action of G on a smooth projective curve Y over k . We say that the KGB obstruction of φ vanishes if G acts on a smooth projective curve X in characteristic  0 in such a way that X / H and Y / H have the same genus for all subgroups H ⊂ G . We determine for which G the KGB obstruction...

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