Duality theories for p-primary etale cohomology III

TL;DR

This paper advances duality theories for p-primary etale cohomology by analyzing nearby cycles on smooth schemes over henselian discrete valuation rings with possibly imperfect residue fields.

Contribution

It extends duality results to cases with non-perfect residue fields, building on previous work from 1986 and 1987.

Findings

Established duality for p-primary etale nearby cycles in new settings

Extended duality theories to non-perfect residue fields

Provided foundational results for further research in p-primary etale cohomology

Abstract

This paper is Part III of the series of work by the first named author on duality theories for p-primary etale cohomology, whose Parts I and II were published in 1986 and 1987, respectively. In this Part III, we study a duality for p-primary etale nearby cycles on smooth schemes over henselian discrete valuation rings of mixed characteristic (0, p) whose residue field is not necessarily perfect.