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arXiv · 1405.7527

Finite polynomial cohomology for general varieties

Amnon Besser·David Loeffler·Sarah Livia Zerbes
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Abstract

Nekovar and Niziol have introduced in [arxiv:1309.7620] a version of syntomic cohomology valid for arbitrary varieties over p-adic fields. This uses a mapping cone construction similar to the rigid syntomic cohomology of the first author in the good-reduction case, but with Hyodo--Kato (log-crystalline) cohomology in place of rigid cohomology. In this short note, we describe a cohomology theory which is a modification of the theory of Nekovar and Niziol, modified by replacing 1 - Phi (where Phi is the Frobenius map) with other polynomials in Phi. This is the analogue for general varieties of the finite-polynomial cohomology defined by the first author for varieties with good reduction. We use this cohomology theory to give formulae for p-adic regulator maps on curves or products of curves, without imposing any good reduction hypotheses.

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Amnon Besser, David Loeffler, Sarah Livia Zerbes. 2014-05-29. Finite polynomial cohomology for general varieties. https://doi.org/10.1007/s40316-015-0041-7

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