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Nekovar and Niziol have introduced in [arxiv:1309.7620] a version of syntomiccohomology valid for arbitrary varieties over p-adic fields. This uses amapping cone construction similar to the rigid syntomic cohomology of the firstauthor 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 modificationof the theory of Nekovar and Niziol, modified by replacing 1 - Phi (where Phiis the Frobenius map) with other polynomials in Phi. This is the analogue forgeneral varieties of the finite-polynomial cohomology defined by the firstauthor for varieties with good reduction. We use this cohomology theory to giveformulae for p-adic regulator maps on curves or products of curves, withoutimposing any good reduction hypotheses.

Finite polynomial cohomology for general varieties