Stratifying derived categories of cochains on certain spaces

TL;DR

This paper advances the understanding of derived categories of cochains on spaces by establishing stratification results that classify subcategories via prime spectra, linking algebraic and topological structures.

Contribution

It presents new stratification theorems for derived categories of ring-spectra and cochains on spaces, connecting algebraic and topological perspectives.

Findings

Stratification of derived category of a ring-spectrum with polynomial homotopy.

Stratification of derived category of cochains on certain spaces.

Topological interpretation of cochain stratification.

Abstract

In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of localizing and thick subcategories in terms of subsets of the prime ideal spectrum of the given ring. In this paper two stratification results are presented: one for the derived category of a commutative ring-spectrum with polynomial homotopy and another for the derived category of cochains on certain spaces. We also give the stratification of cochains on a space a topological content.