Dmitri Orlov mostly deals with Coherent sheaf, Pure mathematics, Derived category, Algebra and Derived algebraic geometry. His work on Coherent sheaf is being expanded to include thematically relevant topics such as Projective test. His study in Homological mirror symmetry and Triangulated category is carried out as part of his studies in Pure mathematics.
Many of his studies involve connections with topics such as Noncommutative geometry and Derived category. He works on Algebra which deals in particular with Sheaf. As part of one scientific family, he deals mainly with the area of Sheaf, narrowing it down to issues related to the Concrete category, and often Direct image with compact support, Closed category and Enriched category.
His scientific interests lie mostly in Pure mathematics, Coherent sheaf, Derived category, Algebra and Homological mirror symmetry. His work focuses on many connections between Pure mathematics and other disciplines, such as Gravitational singularity, that overlap with his field of interest in Algebraic variety. His Coherent sheaf research incorporates elements of Commutative property, Equivalence, Geometry, Bounded function and Abelian group.
His study explores the link between Derived category and topics such as Homotopy category that cross with problems in Adjoint functors. In general Algebra, his work in Sheaf, Abelian category and Scheme is often linked to Derived algebraic geometry linking many areas of study. His Mirror symmetry research includes themes of Cohomology and Brane cosmology.
The scientist’s investigation covers issues in Pure mathematics, Noncommutative geometry, Type, Scheme and Vector bundle. His biological study focuses on Projective test. His study looks at the intersection of Type and topics like Coherent sheaf with Embedding.
The subject of his Scheme research is within the realm of Algebra. The study incorporates disciplines such as Morphism, Differential and Line in addition to Algebra. His work in Vector bundle covers topics such as Quiver which are related to areas like Discrete mathematics and Projective space.
His primary areas of study are Pure mathematics, Projective test, Subcategory, Noncommutative geometry and Scheme. Dmitri Orlov combines subjects such as Function, Vector bundle, Quiver and Endomorphism with his study of Projective test. His biological study spans a wide range of topics, including Characterization, Separable space, Differential and Generator.
His Noncommutative geometry study typically links adjacent topics like Coherent sheaf. His Scheme study combines topics in areas such as Idempotence, Embedding, Global dimension and Differential graded category.
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Semiorthogonal decomposition for algebraic varieties
A. Bondal;D. Orlov.
arXiv: Algebraic Geometry (1995)
TRIANGULATED CATEGORIES OF SINGULARITIES AND D-BRANES IN LANDAU-GINZBURG MODELS
Dmitri O. Orlov.
Proceedings of the Steklov Institute of Mathematics (2004)
Equivalences of derived categories and K3 surfaces
Journal of Mathematical Sciences (1997)
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
Progress in Mathematics (2009)
Reconstruction of a variety from the derived category and groups of autoequivalences
Alexei Bondal;Dmitri Orlov.
Compositio Mathematica (2001)
Derived Categories of Coherent Sheaves
A. Bondal;D. Orlov.
arXiv: Algebraic Geometry (2002)
PROJECTIVE BUNDLES, MONOIDAL TRANSFORMATIONS, AND DERIVED CATEGORIES OF COHERENT SHEAVES
D O Orlov.
Izvestiya: Mathematics (1993)
Mirror symmetry for weighted projective planes and their noncommutative deformations
Denis Auroux;Ludmil Katzarkov;Dmitri O. Orlov.
Annals of Mathematics (2008)
An exact sequence for $K_st^M/2$ with applications to quadratic forms
Dmitri Orlov;Alexander Vishik;Vladimir Voevodsky.
Annals of Mathematics (2007)
Uniqueness of enhancement for triangulated categories
Valery A. Lunts;Dmitri O. Orlov.
Journal of the American Mathematical Society (2010)
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