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Quotients of schemes by \(\alpha _p\) or \(\mu _{p}\) actions in characteristic \(p>0\)

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Abstract

This paper studies integral schemes X defined over a field of characteristic \(p>0\) which admit a nontrivial \(\alpha _p\) or \(\mu _p\) action. In particular, the quotient map \(X \rightarrow Y\) is investigated and structure theorems for it are obtained. Moreover, information on local properties of the quotient Y, like singularities and local Picard groups as well as an adjunction formula for the quotient map are also obtained.

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Author notes

  1. Nikolaos Tziolas

    Present address: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544, USA

Authors and Affiliations

  1. Department of Mathematics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus

    Nikolaos Tziolas

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  1. Nikolaos Tziolas
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Correspondence to Nikolaos Tziolas.

Additional information

The author is supported by a Marie Curie International Outgoing Fellowship, Grant No. PIOF-GA-2013-624345.

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Tziolas, N. Quotients of schemes by \(\alpha _p\) or \(\mu _{p}\) actions in characteristic \(p>0\) . manuscripta math. 152, 247–279 (2017). https://doi.org/10.1007/s00229-016-0854-y

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  • DOI: https://doi.org/10.1007/s00229-016-0854-y

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