Computing homological residue fields in algebra and topology

TL;DR

This paper explores the computation of homological residue fields within tensor-triangular geometry across various mathematical contexts, including topology and group theory.

Contribution

It provides explicit calculations of homological residue fields in several key examples, advancing understanding in tensor-triangular geometry.

Findings

Explicit descriptions of homological residue fields in stable homotopy theory

Calculations in modular representation theory of finite groups

Broader insights into tensor-triangular geometric structures

Abstract

We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.