Reduction and lifting problem for differential forms on Berkovich curves
| Autor: | Temkin, Michael, Tyomkin, Ilya |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2022.108208 |
| Popis: | Given a complete real-valued field $k$ of residue characteristic zero, we study properties of a differential form $\omega$ on a smooth proper $k$-analytic curve $X$. In particular, we associate to $(X,\omega)$ a natural tropical reduction datum combining tropical data of $(X,\omega)$ and algebra-geometric reduction data over the residue field $\widetilde{k}$. We show that this datum satisfies natural compatibility condition, and prove a lifting theorem asserting that any compatible tropical reduction datum lifts to an actual pair $(X,\omega)$. In particular, we obtain a short proof of the main result of a work [BCGGM20] by Bainbridge, Chen, Gendron, Grushevsky, and M\"oller. Comment: 19 pages, final version, published in Advances in Mathematics |
| Databáze: | arXiv |
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