Orbifold Semiorthogonal Decompositions for Abelian Varieties

TL;DR

This paper constructs orbifold semiorthogonal decompositions for derived categories of quotients of Abelian varieties by finite groups, leveraging recent classification results to handle specific group actions.

Contribution

It introduces a new method for constructing semiorthogonal decompositions in orbifold settings for Abelian varieties with certain group actions.

Findings

Established orbifold semiorthogonal decompositions for $\, ext{D}[A/G]$

Applied recent classification results to specific group actions

Extended semiorthogonal decomposition techniques to orbifold cases

Abstract

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal decomposition for $\mathcal{D}[A/G]$ provided $G = T\rtimes H$ with $T$ a subgroup of translations and $H$ is a subgroup of group automorphisms.