A Rickard equivalence for hopfological homotopy categories

TL;DR

This paper demonstrates that the homotopy category in hopfological algebra can be realized as a Verdier quotient of its derived category, extending Rickard's approach to a new algebraic context.

Contribution

It introduces a new realization of the hopfological homotopy category as a Verdier quotient, generalizing Rickard's stable module category construction.

Findings

Homotopy category in hopfological algebra is a Verdier quotient.

Extends Rickard's realization to hopfological algebra.

Provides a new perspective on homotopy categories in algebra.

Abstract

In his paper [Ric89], Rickard presents the stable module category of a self-injective algebra as a Verdier quotient of its derived category by perfect complexes. We present a similar realization of the homotopy category in hopfological algebra as such a Verdier quotient.