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arXiv · 2404.08578

Classification and nonexistence for $t$-structures on derived categories of schemes

Alexander Clark·Pat Lank·Kabeer Manali-Rahul·Chris J. Parker
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Abstract

Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-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 $t$-structures.

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Alexander Clark, Pat Lank, Kabeer Manali-Rahul, Chris J. Parker. 2024-04-12. Classification and nonexistence for $t$-structures on derived categories of schemes. https://arxiv.org/abs/2404.08578

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