Hochschild dimensions of tilting objects

TL;DR

This paper establishes a new upper bound for the generation time of tilting objects and applies it to verify a conjecture related to the Rouquier dimension of derived categories on smooth varieties.

Contribution

Introduces a novel upper bound for tilting objects' generation time and confirms a conjecture of Orlov in new cases.

Findings

New upper bound for tilting objects' generation time

Verification of Orlov's conjecture in additional cases

Enhanced understanding of Rouquier dimension in derived categories

Abstract

We give a new upper bound for the generation time of a tilting object and use it to verify, in some new cases, a conjecture of Orlov on the Rouquier dimension of the derived category of coherent sheaves on a smooth variety.