A note on Serre duality and equivariantization

TL;DR

This paper explicitly computes Serre duality in abelian categories with finite group actions, explores special cases including periodic Serre duality, and discusses examples and implications of equivariantization.

Contribution

It provides explicit formulas for Serre duality on equivariant categories and analyzes the effects of group actions on duality properties.

Findings

Explicit computation of Serre duality on equivariant categories

Analysis of periodic Serre duality under equivariantization

Discussion of examples illustrating the theory

Abstract

For an abelian category with a Serre duality and a finite group action, we compute explicitly the Serre duality on the category of equivariant objects. Special cases and examples are discussed. In particular, an abelian category with a periodic Serre duality and its equivariantization are studied.