Syzygies in equivariant cohomology in positive characteristic

TL;DR

This paper develops a new algebraic framework for understanding syzygies in equivariant cohomology over fields of positive characteristic, extending existing theories to p-tori and providing insights into the Atiyah-Bredon sequence.

Contribution

It introduces a novel algebraic approach to syzygies in equivariant cohomology, applicable to p-tori and coefficients in _p, and advances the understanding of the Atiyah-Bredon sequence's partial exactness.

Findings

Extended syzygy theory to p-tori and _p coefficients.

Provided a new algebraic method for partial exactness of the Atiyah-Bredon sequence.

Unified previous cases within a broader algebraic framework.

Abstract

We develop a theory of syzygies in equivariant cohomology for tori as well as $p$-tori and coefficients in $\mathbb{F}_p$. A noteworthy feature is a new algebraic approach to the partial exactness of the Atiyah-Bredon sequence, which also covers all instances considered so far.