22 October 2025 — Verona

Conservative geometric tt-functors via purity

Juan Omar Gomez, University of Bielefeld

Abstract

Given a family of coproduct-preserving tensor-triangulated (tt) functors between rigidly-compactly generated tt-categories (also called geometric tt-functors), it is natural to ask when they are jointly conservative. Such joint conservativity is the minimal requirement for attempting to descend tt-geometric information along the family. In this talk, I will present a criterion for this property in terms of purity in tt-categories, highlighting its homological flavor.

As an application, we establish a Chouinard-type theorem for module categories over cochains on discrete \(p\)-toral groups. This result yields a classification of localizing and thick tensor ideals in terms of the homogeneous spectrum of the cochain algebra. The talk is based on ongoing joint work with Natalia Castellana.