Integral p-adic cohomology theories for open and singular varieties
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910826030432256 |
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| author | Ertl, Veronika Shiho, Atsushi Sprang, Johannes |
| author_facet | Ertl, Veronika Shiho, Atsushi Sprang, Johannes |
| contents | For open and singular varieties in positive characteristic p we study the existence of an integral p-adic cohomology theory which is finitely generated, compatible with log crystalline cohomology and rationally compatible with rigid cohomology. We develop such a theory under certain assumptions of resolution of singularities in positive characteristic, by using cdp- and cdh-topologies.
Without resolution of singularities in positive characteristic, we prove the existence of a good p-adic cohomology theory for open and singular varieties in cohomological degree 1, by using split proper generically étale hypercoverings. This is a slight generalisation of a result due to Andreatta--Barbieri-Viale. We also prove that this approach does not work for higher cohomological degrees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_11009 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Integral p-adic cohomology theories for open and singular varieties Ertl, Veronika Shiho, Atsushi Sprang, Johannes Number Theory Algebraic Geometry 14F30, 14E15, 14F20, 18F10 For open and singular varieties in positive characteristic p we study the existence of an integral p-adic cohomology theory which is finitely generated, compatible with log crystalline cohomology and rationally compatible with rigid cohomology. We develop such a theory under certain assumptions of resolution of singularities in positive characteristic, by using cdp- and cdh-topologies. Without resolution of singularities in positive characteristic, we prove the existence of a good p-adic cohomology theory for open and singular varieties in cohomological degree 1, by using split proper generically étale hypercoverings. This is a slight generalisation of a result due to Andreatta--Barbieri-Viale. We also prove that this approach does not work for higher cohomological degrees. |
| title | Integral p-adic cohomology theories for open and singular varieties |
| topic | Number Theory Algebraic Geometry 14F30, 14E15, 14F20, 18F10 |
| url | https://arxiv.org/abs/2105.11009 |