The geometric Merkurjev-Panin Conjecture for the Cox category

TL;DR

This paper proves that the full strong exceptional collection of Bondal-Thomsen line bundles remains invariant under lattice automorphisms in the Cox category of a projective toric variety, supporting the Cox category's role in homological algebra.

Contribution

It establishes a strong version of the geometric Merkurjev-Panin conjecture for the Cox category, demonstrating invariance of exceptional collections under automorphisms.

Findings

Invariance of exceptional collections under lattice automorphisms

Supports Cox category as a natural setting for homological algebra

Advances understanding of derived categories in toric geometry

Abstract

We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exceptional collection of Bondal-Thomsen line bundles is invariant under the group of lattice automorphisms that permute the rays of the toric variety's fan. Our result is meant to further illustrate that the Cox category is a natural repository for homological algebra on toric varieties.