Ordinary K3 surfaces over a finite field
| Authors | |
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| Publication date | 04-2020 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | Issue number | 2020 | 761 |
| Pages (from-to) | 141-161 |
| Organisations |
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| Abstract | We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Our main result is conditional on a conjecture on potential semi-stable reduction of K3 surfaces over p-adic fields. We give unconditional versions for K3 surfaces of large Picard rank and for K3 surfaces of small degree. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1515/crelle-2018-0023 |
| Published at | https://arxiv.org/abs/1711.09225 |
| Other links | https://www.scopus.com/pages/publications/85055642924 |
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