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, Volume 154, Issue 1–2, pp 13–22 | Cite as

The moduli of smooth hypersurfaces with level structure

Article

Abstract

We construct the moduli space of smooth hypersurfaces with level N structure over \(\mathbb {Z}[1/N]\). As an application we show that, for N large enough, the stack of smooth hypersurfaces over \(\mathbb {Z}[1/N]\) is uniformisable by a smooth affine scheme. To prove our results, we use the Lefschetz trace formula to show that automorphisms of smooth hypersurfaces act faithfully on their cohomology. We also prove a global Torelli theorem for smooth cubic threefolds over fields of odd characteristic.

Mathematics Subject Classification

14D23 (14K30, 14J50, 14C34) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut für MathematikJohannes Gutenberg-Universität MainzMainzGermany
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

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