Homotopy Epimorphisms and Derived Tate's Acyclicity for Commutative C*-algebras
Algebraic Geometry
2021-03-23 v1 Category Theory
Functional Analysis
Abstract
We study homotopy epimorphisms and covers formulated in terms of derived Tate's acyclicity for commutative C*-algebras and their non-Archimedean counterparts. We prove that a homotopy epimorphism between commutative C*-algebras precisely corresponds to a closed immersion between the compact Hausdorff topological spaces associated to them, and a cover of a commutative C*-algebra precisely corresponds to a topological cover of the compact Hausdorff topological space associated to it by closed immersions admitting a finite subcover. This permits us to prove derived and non-derived descent for Banach modules over commutative C*-algebras.
Keywords
Cite
@article{arxiv.2103.11722,
title = {Homotopy Epimorphisms and Derived Tate's Acyclicity for Commutative C*-algebras},
author = {Federico Bambozzi and Tomoki Mihara},
journal= {arXiv preprint arXiv:2103.11722},
year = {2021}
}