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 padic fields. This uses a mapping cone construction similar to the rigid syntomic cohomology of the first author in the goodreduction case, but with HyodoKato (logcrystalline) 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 finitepolynomial cohomology defined by the first author for varieties with good reduction. We use this cohomology theory to give formulae for padic regulator maps on curves or products of curves, without imposing any good reduction hypotheses.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.7527
 Bibcode:
 2014arXiv1405.7527B
 Keywords:

 Mathematics  Number Theory
 EPrint:
 Ann. math. du Qu\'ebec 40 (2016), no. 1, 203220