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.