Spectral and homological properties of Hilbert modules over the disc algebra

TL;DR

This paper investigates the spectral and homological characteristics of Hilbert modules over the disc algebra, providing conditions for extension group vanishing and insights into projective modules and derivation problems.

Contribution

It introduces spectral conditions for extension groups and advances understanding of projective Hilbert modules over the disc algebra.

Findings

Spectral conditions for vanishing extension groups

Insights into the structure of projective Hilbert modules

Progress on the classical derivation problem

Abstract

We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective Hilbert modules. Part of our work also addresses the classical derivation problem.