Homological Bondal-Orlov localization conjecture for rational singularities
Given a resolution of rational singularities π:X~→X over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor Rπ∗:Db(X~)→Db(X)
between bounded derived categories of coherent sheaves generates Db(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 π:X~→X , with X~
smooth, satisfying Rπ∗(OX~)=OX .
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Cambridge University Press
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