English

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 tt-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such tt-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 tt-structures.

Keywords

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

R2 v1 2026-06-28T15:52:40.666Z