Proper base change over henselian pairs

TL;DR

This paper addresses a specific proper base change problem over henselian pairs, providing a solution in a non-affine case, contributing to algebraic geometry and étale cohomology theory.

Contribution

It offers a new solution to proper base change over henselian pairs in a non-affine setting, expanding understanding in algebraic geometry.

Findings

Proposes a solution to proper base change in a non-affine context

Extends the theory of étale cohomology over henselian pairs

Addresses a question from the Séminaire de Géométrie Algébrique

Abstract

We discuss a question which appears in [S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bous Marie- Th\'eorie des topos et cohomologie \'etale des sch\'emas, Expos\'e XII, Remarks 6.13] concerning proper base change. In particular, we propose a solution in a particular non-affine case.