Theorems A and B for dagger quasi-Stein spaces

Abstract

In this article, we use the homological methods of the theory of quasi-abelian categories and 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 Kiehl's proof for rigid quasi-Stein spaces.