algebraic geometry

Proxy smallness meets -structures

arXiv:2605.26057

summary

The paper defines proxy smallness for t‑structures on triangulated categories over a Noetherian scheme, using tensor actions, and uses this to characterize locally complete intersection schemes and classify preaisles in the bounded derived category of coherent sheaves.

Abstract

We introduce a notion of proxy smallness for -structures on triangulated categories associated to a Noetherian scheme. Specifically, the theory is developed in the presence of tensor actions. Consequently, our results yield a new characterization of schemes that are locally complete intersections in terms of -structures, as well as a topological classification of preaisles on the bounded derived category of coherent sheaves.

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Topics & keywords

#t-structures#triangulated categories#derived categories#locally complete intersections#preaisles#tensor actionsproxy smallnesst-structuretriangulated categoryNoetherian schemederived category of coherent sheavespreaisle
Proxy smallness meets $t$-structures · wovepaper