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arXiv · 2608.22539

The Bondal-Orlov Localization Conjecture Holds for Threefolds

Yu Shen·Tianyang Sun
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Abstract

Let $X$ be a noetherian scheme with the resolution property, and let $p:Y\to X$ be a projective morphism. Suppose that $R^{i}p_{*}=0$ for $i>2$ and that $ \mathcal {O}_{X}\longrightarrow Rp_{*}\mathcal {O}_{Y} $ is an isomorphism. We show that derived pushforward induces an equivalence \[ D^{b}(Y)/\operatorname{Ker}(Rp_{*})\simeq D^{b}(X). \] As an application, we prove a characteristic-free form of the Bondal--Orlov localization conjecture for quasi-projective threefolds.

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Yu Shen, Tianyang Sun. 2026-08-23. The Bondal-Orlov Localization Conjecture Holds for Threefolds. https://arxiv.org/abs/2608.22539

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