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arXiv · 2105.11009

Integral p-adic cohomology theories for open and singular varieties

Veronika Ertl·Atsushi Shiho·Johannes Sprang
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Abstract

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 \'etale 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.

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Veronika Ertl, Atsushi Shiho, Johannes Sprang. 2021-05-23. Integral p-adic cohomology theories for open and singular varieties. https://arxiv.org/abs/2105.11009

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