Poincar\'{e} duality for rigid analytic Hyodo--Kato theory
Abstract
The purpose of this paper is to establish Hyodo--Kato theory with compact support for semistable schemes through rigid analytic methods. To this end we introduce several types of log rigid cohomology with compact support. moreover we show that additional structures on the (rigid) Hyodo--Kato cohomology and the Hyodo--Kato map introduced in our previous paper are compatible with Poincar\'{e} duality. Compared to the crystalline approach, the constructions are explicit yet versatile, and hence suitable for computations.
Cite
@article{arxiv.2009.09160,
title = {Poincar\'{e} duality for rigid analytic Hyodo--Kato theory},
author = {Veronika Ertl and Kazuki Yamada},
journal= {arXiv preprint arXiv:2009.09160},
year = {2024}
}
Comments
4th version, 58 pages. We added an appendix concerning an explicit construction of the cup product. We modified the references to our paper "Rigid analytic reconstruction of Hyodo--Kato theory" where necessary. We made changes to avoid the use of Thms. A and B for dagger quasi-Stein spaces