The moduli of smooth hypersurfaces with level structure

The moduli of smooth hypersurfaces with level structure We construct the moduli space of smooth hypersurfaces with level N structure over $$\mathbb {Z}[1/N]$$ Z [ 1 / N ] . As an application we show that, for N large enough, the stack of smooth hypersurfaces over $$\mathbb {Z}[1/N]$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

The moduli of smooth hypersurfaces with level structure

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
D.O.I.
10.1007/s00229-016-0906-3
Publisher site
See Article on Publisher Site

Abstract

We construct the moduli space of smooth hypersurfaces with level N structure over $$\mathbb {Z}[1/N]$$ Z [ 1 / N ] . As an application we show that, for N large enough, the stack of smooth hypersurfaces over $$\mathbb {Z}[1/N]$$ 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.

Journal

Manuscripta MathematicaSpringer Journals

Published: Dec 19, 2016

References

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