Tensor triangular geometry of modules over the mod 2 Steenrod algebra

TL;DR

This paper computes the Balmer spectrum of a tensor triangulated category of comodules over the mod 2 dual Steenrod algebra, classifying thick subcategories and resolving a conjecture of Palmieri.

Contribution

It provides the first explicit computation of the Balmer spectrum for this category, advancing tensor triangular geometry in algebraic topology.

Findings

Classified the thick subcategories of comodules over the mod 2 dual Steenrod algebra.

Resolved Palmieri's conjecture regarding the structure of these subcategories.

Established a framework for further tensor triangular geometry studies in algebraic topology.

Abstract

We compute the Balmer spectrum of a certain tensor triangulated category of comodules over the mod 2 dual Steenrod algebra. This computation effectively classifies the thick subcategories, resolving a conjecture of Palmieri.