Auslander-Reiten sequences for homotopists and arithmeticians
Sunil Chebolu, J\'an Min\'a\v{c}
TL;DR
This paper introduces Auslander-Reiten sequences in the context of group algebras, connecting homotopy theory and Galois theory, and explores their applications in Tate cohomology and arithmetic objects.
Contribution
It extends Auslander-Reiten theory to group algebras and links it to homotopy and Galois theories, providing new insights and applications.
Findings
New applications of Auslander-Reiten sequences in Tate cohomology
Connections established between homotopy theory and Galois theory
Interpretation of sequences in arithmetic contexts
Abstract
We introduce Auslander-Reiten sequences for group algebras and give several recent applications. The first part of the paper is devoted to some fundamental problems in Tate cohomology which are motivated by homotopy theory. In the second part of the paper we interpret Auslander-Reiten sequences in the context of Galois theory and connect them to some important arithmetic objects.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Advanced Topics in Algebra