The moduli of smooth hypersurfaces with level structure
The moduli of smooth hypersurfaces with level structure
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具有水平结构的光滑超曲面的模
DOI：
10.1007/s00229-016-0906-3
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发表时间：
2015
影响因子：
0.6
通讯作者：
D. Loughran
中科院分区：
文献类型：
--
作者：
A. Javanpeykar;D. Loughran
We construct the moduli space of smooth hypersurfaces with level N structure over Z[1/N]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}[1/N]$$\end{document}. As an application we show that, for N large enough, the stack of smooth hypersurfaces over Z[1/N]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}[1/N]$$\end{document} 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.
We construct the moduli space of smooth hypersurfaces with level N structure over Z[1/N]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}[1/N]$$\end{document}. As an application we show that, for N large enough, the stack of smooth hypersurfaces over Z[1/N]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}[1/N]$$\end{document} 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.