Classification and nonexistence for $t$-structures on derived categories of schemes
Algebraic Geometry
2026-05-19 v5 Category Theory
Abstract
Given a suitable Noetherian scheme, we classify tensor -structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such -structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor -structures.
Cite
@article{arxiv.2404.08578,
title = {Classification and nonexistence for $t$-structures on derived categories of schemes},
author = {Alexander Clark and Pat Lank and Kabeer Manali-Rahul and Chris J. Parker},
journal= {arXiv preprint arXiv:2404.08578},
year = {2026}
}
Comments
Improved classification, minor cosmetic changes, change to intro