Theorems A and B for dagger quasi-Stein spaces

TL;DR

This paper proves Theorems A and B for dagger quasi-Stein spaces using homological methods and functional analysis, extending Kiehl's approach for rigid quasi-Stein spaces.

Contribution

It introduces a homological framework to establish Theorems A and B for dagger quasi-Stein spaces, generalizing previous proofs.

Findings

Theorems A and B hold for a broad class of dagger quasi-Stein spaces.

Derived functors of the projective limit vanish under certain conditions.

The proof framework generalizes Kiehl's method for rigid spaces.

Abstract

In this article we use the homological methods of the theory of quasi-abelian categories and some results from functional analysis to prove Theorems A and B for (a broad sub-class of) dagger quasi-Stein spaces. In particular we show how to deduce these theorems from the vanishing, under certain hypothesis, of the higher derived functors of the projective limit functor. Our strategy of the proof generalizes and puts in a more formal framework the Kiehl's proof for rigid quasi-Stein spaces.