  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.
