Proper pushforwards on analytic adic spaces

TL;DR

This paper develops proper pushforward operations for morphisms of analytic adic spaces, extending existing rigid analytic theory, and constructs trace maps and duality pairings for smooth, partially proper morphisms.

Contribution

It generalizes the theory of proper pushforwards from rigid analytic varieties to analytic adic spaces, including the construction of trace maps and duality pairings.

Findings

Constructed proper pushforwards for partially proper morphisms of analytic adic spaces.

Extended van der Put's theory from rigid analytic varieties to adic spaces.

Developed trace maps and duality pairings for smooth, partially proper morphisms.

Abstract

We construct proper pushforwards for partially proper morphisms of analytic adic spaces. This generalises the theory due to van der Put in the case of rigid analytic varieties over a non-Archimedean field. For morphisms which are smooth and partially proper in the sense of Kiehl, we furthermore construct the trace map and duality pairing.