Poincar\'{e} duality for rigid analytic Hyodo--Kato theory

TL;DR

This paper develops a version of Hyodo--Kato theory with compact support for semistable schemes using rigid analytic methods, establishing Poincaré duality and compatible structures for explicit computations.

Contribution

It introduces log rigid cohomology with compact support and demonstrates compatibility of structures with Poincaré duality in the rigid analytic setting.

Findings

Established Hyodo--Kato theory with compact support for semistable schemes.

Proved compatibility of additional structures with Poincaré duality.

Provided explicit, versatile constructions suitable for computations.

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.