Models of $\mu_{p^2,K}$ over a discrete valuation ring

Abstract : Let R be a discrete valuation ring with residue field of characteristic p>0. Let K be its fraction field. We prove that any finite and flat R-group scheme, isomorphic to \mu_{p^2,K} on the generic fiber, is the kernel in a short exact sequence which generically coincides with the Kummer sequence. We will explicitly describe and classify such models. In the appendix X. Caruso shows how to classify models of \mu_{p^2,K}, in the case of unequal characteristic, using the Breuil-Kisin theory.
Mots-clés : schémas en groupes
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Contributor : Dajano Tossici <>
Submitted on : Tuesday, April 1, 2014 - 6:27:21 PM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM

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  • HAL Id : hal-00968922, version 1
  • ARXIV : 1001.1416

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Dajano Tossici. Models of $\mu_{p^2,K}$ over a discrete valuation ring. Journal of Algebra, Elsevier, 2010, 323 (7), pp.1908-1957. 〈hal-00968922〉

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