Cosupport in tensor triangular geometry

TL;DR

This paper develops a dual theory of cosupport in tensor triangular geometry, revealing deep relationships with support and establishing costratification for various algebraic, topological, and geometric categories.

Contribution

It introduces a comprehensive framework for cosupport, demonstrating its importance alongside support, and develops descent techniques to prove costratification in multiple mathematical contexts.

Findings

Support and cosupport are categorically dual concepts.

Many categories are shown to be costratified.

Descent techniques are effective for establishing costratification.

Abstract

We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and discover surprising relations between the theory of costratification and the theory of stratification. We prove that many categories in algebra, topology and geometry are costratified by developing and applying descent techniques. An overarching theme is that cosupport is relevant for diverse questions in tensor triangular geometry and that a full understanding of a category requires knowledge of both its support and its cosupport.