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Realizing deformations of curves using Lubin-Tate formal groups

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Abstract

Letk be an algebraically closed field of characteristicp>0 andR be a suitable valuation ring of characteristic 0, dominating the Witt vectorsW(k). We show how Lubin-Tate formal groups can be used to lift those orderp n automorphisms ofk[[Z]] toR[[Z]], which occur as endomorphisms of a formal group overk of suitable height. We apply this result to prove the existence of smooth liftings of galois covers of smooth curves from characteristicp to characteristic 0, provided thep-part of the inertia groups acting on the completion of the local rings at the points of the cover overk arep-power cyclic and determined by an endomorphism of a suitable formal group overk.

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Authors and Affiliations

  1. Department of Mathematics, University of Stellenbosch, 7602, Stellenbosch, South Africa

    Barry Green

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  1. Barry Green
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Correspondence to Barry Green.

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The author would like to express his thanks to the Max-Planck-Institut für Mathematik, Bonn, for its hospitality and support, where this research was done during a visit from June – September 2001.

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Green, B. Realizing deformations of curves using Lubin-Tate formal groups. Isr. J. Math. 139, 139–148 (2004). https://doi.org/10.1007/BF02787544

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  • DOI: https://doi.org/10.1007/BF02787544

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