Abstract
We construct the moduli space of smooth hypersurfaces with level N
structure over Z[1=N]. As an application we show that, for N large enough, the stack of smooth hypersurfaces over Z[1=N] is uniformisable by a smooth ane 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 elds of odd characteristic.
structure over Z[1=N]. As an application we show that, for N large enough, the stack of smooth hypersurfaces over Z[1=N] is uniformisable by a smooth ane 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 elds of odd characteristic.
Original language | English |
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Number of pages | 16 |
Journal | Manuscripta Mathematica |
Early online date | 19 Dec 2016 |
DOIs | |
Publication status | Published - 2016 |