Preservation for generation along the structure morphism of coherent algebras over a scheme
Algebraic Geometry
2025-03-26 v4 Commutative Algebra
Rings and Algebras
Representation Theory
Abstract
This work demonstrates classical generation is preserved by the derived pushforward along the structure morphism of a noncommutative coherent algebra to its underlying scheme. Additionally, we establish that the Krull dimension of a variety over a field is a lower bound for the Rouquier dimension of the bounded derived category associated with a noncommutative coherent algebra on it. This is an extension of a classical result of Rouquier to the noncommutative context.
Keywords
Cite
@article{arxiv.2312.02840,
title = {Preservation for generation along the structure morphism of coherent algebras over a scheme},
author = {Anirban Bhaduri and Souvik Dey and Pat Lank},
journal= {arXiv preprint arXiv:2312.02840},
year = {2025}
}
Comments
Current version: Accepted to Bull. Lon. Math. Soc., pre-final, title change. Previous version: Fixed minor typos