Geodesic
Homological Bondal-Orlov localization conjecture for rational singularities
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

Given a resolution of rational singularities $\pi \colon {\tilde {X}} \to X$ over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor ${\mathbf {R}}\pi _*\colon {\mathbf {D}}^{\mathrm {b}}({\tilde {X}}) \to {\mathbf {D}}^{\mathrm {b}}(X)$ between bounded derived categories of coherent sheaves generates ${\mathbf {D}}^{\mathrm {b}}(X)$ as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms $\pi \colon {\tilde {X}} \to X$, with ${\tilde {X}}$ smooth, satisfying ${\mathbf {R}}\pi _*({\mathcal {O}}_{\tilde {X}}) = {\mathcal {O}}_X$. 
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     author = {Mirko Mauri and Evgeny Shinder},
     title = {Homological {Bondal-Orlov} localization conjecture for rational singularities},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.65},
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Mirko Mauri; Evgeny Shinder. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.65

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