Finite polynomial cohomology for general varieties
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.
Cite
@article{arxiv.1405.7527,
title = {Finite polynomial cohomology for general varieties},
author = {Amnon Besser and David Loeffler and Sarah Livia Zerbes},
journal= {arXiv preprint arXiv:1405.7527},
year = {2018}
}