Cyclic extensions and the local lifting problem

Abstract

The local Oort conjecture states that, if $\Gamma$ is cyclic and $k$ is an algebraically closed field of characteristic $p$, then all $\Gamma$-extensions of $k[[t]]$ should lift to characteristic zero. We prove a critical case of this conjecture. In particular, we show that the conjecture is always true when $v_p(|\Gamma|) \leq 3$ and is true for arbitrarily highly $p$-divisible cyclic groups $\Gamma$ when a certain condition on the higher ramification filtration is satisfied.

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      AUTHOR = {Tossici, Dajano},
      TITLE = {Models of {$\mu\sb {p\sp 2,K}$} over a discrete valuation ring},
      NOTE = {with an appendix by Xavier Caruso},
      JOURNAL = {J. Algebra},
      FJOURNAL = {Journal of Algebra},
      VOLUME = {323},
      YEAR = {2010},
      NUMBER = {7},
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      ISSN = {0021-8693},
      CODEN = {JALGA4},
      MRCLASS = {14L15},
      MRNUMBER = {2594655},
      MRREVIEWER = {Alan Koch},
      ZBLNUMBER = {1193.14059},
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      year={2013},
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      publisher={Springer-Verlag},
      ADDRESS={New York},
      keywords={11S15; 11S31; 14F05; 19F05},
      author={Wewers, Stefan},
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    @book {ZariskiSamuelII, MRKEY = {0389876},
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      TITLE = {Commutative Algebra. {V}ol. {II}},
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      MRNUMBER = {0389876},
      ZBLNUMBER = {0322.13001},
      DOI = {10.1007/978-3-662-29244-0},
      }

Authors

Andrew Obus

Department of Mathematics, University of Virginia, Charlottesville VA 22904

Stefan Wewers

Institut für Reine Mathematik, Universität Ulm, 89081 Ulm, Germany