Article ID Journal Published Year Pages File Type
4598366 Journal of Pure and Applied Algebra 2007 8 Pages PDF
Abstract

We give a relation between the dimension of the tangent space of the deformation functor of curves with automorphisms and the Galois module structure of the space of 2-holomorphic differentials. We prove a homological version of the local–global principle similar to the one of J. Bertin and A. Mézard. Let GG be a cyclic subgroup of the group of automorphisms of a curve XX, so that the order of GG is equal to the characteristic. By using the results of S. Nakajima on the Galois module structure of the space of 2-holomorphic differentials, we compute the dimension of the tangent space of the deformation functor.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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