Triangular spectrum of some triangulated categories

TL;DR

This paper computes the triangular spectrum of specific tensor triangulated categories relevant in algebraic geometry, including categories of equivariant sheaves and split superschemes, providing new insights into their structure.

Contribution

It introduces the computation of the triangular spectrum for categories of G-equivariant sheaves and split superschemes, expanding the understanding of their tensor triangulated structure.

Findings

Triangular spectrum computed for G-equivariant sheaves on smooth schemes.

Triangular spectrum computed for derived categories of split superschemes.

Provides new tools for analyzing tensor triangulated categories in algebraic geometry.

Abstract

In this paper, we compute triangular spectrum (as defined by P. Balmer) of two classes of tensor triangulated categories which are quite common in algebraic geometry. One of them is the derived category of $G$-equivariant sheaves on a smooth scheme $X$ for a finite group $G$ which acts on $X$ with some smoothness condition on the quotient. The other class is the derived category of split superschemes.