A variety that cannot be dominated by one that lifts
| Autor: | de Bruyn, Remy van Dobben |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove a precise version of a theorem of Siu and Beauville on morphisms to higher genus curves, and use it to show that if a variety $X$ in characteristic $p$ lifts to characteristic $0$, then any morphism $X \to C$ to a curve of genus $g \geq 2$ can be lifted along. We use this to construct, for every prime $p$, a smooth projective surface $X$ over $\bar{\mathbb F}_p$ that cannot be rationally dominated by a smooth proper variety $Y$ that lifts to characteristic $0$. Comment: 26 pages. Fixed typos, added references, and expanded introduction. This is the main result of the author's dissertation (2018) |
| Databáze: | arXiv |
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