Equiramified deformations of covers in positive characteristic


Suppose φ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of φ in equal characteristic, which are equiramified in that the branch locus is constant and the ramification filtration is fixed. We show that the moduli space Mφ parametrizing equiramified deformations of φ is a subscheme of an explicitly constructed scheme. This allows us to give an explicit upper and lower bound for the Krull dimension dφ of Mφ. These bounds depend only on the ramification filtration of φ. When φ is an abelian p-group cover, we use class field theory to show that the upper bound for dφ is realized. 2000 Mathematical Subject Classification: 14H30, 14G32

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@inproceedings{Pries2005EquiramifiedDO, title={Equiramified deformations of covers in positive characteristic}, author={Rachel J. Pries}, year={2005} }