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11 papers · 2 filters
Categorical resolutions of irrational singularities
Alexander Kuznetsov, Valery A. Lunts
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiortho…
Ga-actions on affine cones
Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg
We give a criterion of existence of a unipotent group action on the affine cone over a projective variety or, more generally, on the affine quasicone over a variety which is projec…
Height of exceptional collections and Hochschild cohomology of quasiphantom categories
Alexander Kuznetsov
We define the normal Hochschild cohomology of an admissible subcategory of the derived category of coherent sheaves on a smooth projective variety --- a graded vector space whi…
A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
Roman Fedorov, Ivan Panin
Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over t…
Commuting differential operators and higher-dimensional algebraic varieties
Herbert Kurke, Denis Osipov, Alexander Zheglov
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how…
Geometric Phantom Categories
Sergey Gorchinskiy, Dmitri Orlov
In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective variet…