Besser, A;
Loeffler, D;
Zerbes, SL;
(2016)
Finite polynomial cohomology for general varieties.
Annales mathématiques du Québec
, 40
(1)
pp. 203-220.
10.1007/s40316-015-0041-7.
Preview |
Text
1405.7527v2.pdf - Published Version Download (224kB) | Preview |
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.
| Type: | Article |
|---|---|
| Title: | Finite polynomial cohomology for general varieties |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40316-015-0041-7 |
| Publisher version: | http://dx.doi.org/10.1007/s40316-015-0041-7 |
| Language: | English |
| Additional information: | © The Author(s) 2016. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Finite-polynomial cohomology; Syntomic cohomology; Regulators |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1436873 |
Archive Staff Only
 |
View Item |
