Dmitri Olegowitsch Orlov

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Dmitri Olegowitsch Orlov , Russian Дмитрий Олегович Орлов , English transcription Dmitri Olegovich Orlov, (born September 19, 1966 in Vladimir ) is a Russian mathematician .

Orlow received his doctorate in 1991 from Lomonosov University under Vasily Alexejewitsch Iskowskich (and Alexei Igorewitsch Bondal ). In 2002 he completed his habilitation (Russian doctorate). He is at the Steklov Institute in Moscow.

He deals with homological algebra ( derived and triangulated categories ), algebraic geometry ( derived algebraic geometry , mirror symmetry , quasi-coherent sheaves ) and non-commutative geometry. He is a pioneer of category theory under development, the commutative and non-commutative geometry over algebraic enhanced triangulated categories (English: enhanced triangulated categories) connects of quasi-coherent sheaves. With Alexei Bondal he proved a reconstruction theorem named after them for smooth varieties from derived categories of coherent sheaves.

Alexander Iwanowitsch Efimow (Efimov) is one of his doctoral students .

He was invited speaker at the International Congress of Mathematicians in Beijing (Derived categories of coherent sheaves, with A. Bondal).

Fonts (selection)

  • with A. Bondal: Semi-orthogonal decomposition for algebraic varieties, Arxiv , 1995
  • with A. Bondal: Reconstruction of a variety from the derived category and groups of autoequivalences , Compositio Math., Volume 125, 2001, pp. 327-344, Arxiv
  • with AI Bondal: Derived categories of coherent sheaves, Proc. Boarding school Congress of Mathematicians, Beijing, 2002, Arxiv
  • Quasi-coherent sheaves in commutative and non-commutative geometry, Izv. RAN. Ser. Mat., Vol. 67, 2003, pp. 119-138
  • Derived categories of coherent sheaves and equivalences between them,, Russian Mathematical Surveys, Volume 58, 2003, p. 511
  • with AN Kapustin : Lectures on mirror symmetry, derived categories, and D-branes, Russian Mathematical Surveys, Volume 59, 2004, pp. 907–940, Arxiv
  • Derived categories of coherent sheaves and motives , Russian Mathematical Surveys, Volume 60, 2005, pp. 1242-1244, Arxiv
  • with VA Lunts, AI Efimov: Deformation theory of objects in homotopy and derived categories, Part 1, Advances in Mathematics, Volume 222, 2009, pp. 359-401, Arxiv , Part 2, Volume 224, 2010, pp. 45-102 , Arxiv , Part 3, Volume 226, 2011, pp. 3857-3911, Arxiv
  • with Valery A. Lunts: Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc., Vol. 23, 2010, pp. 853-908, Arxiv
  • Formal completions and idempotent completions of triangulated categories of singularities ,, Adv. Math., Volume 226, 2011, pp. 206-217, Arxiv
  • Landau-Ginzburg Models, D-branes, and Mirror Symmetry , Mat. Contemp., Volume 41, 2012, pp. 75–112, Arxiv
  • Derived noncommutative schemes, geometric realizations, and finite dimensional algebras , Russian Math. Surveys, Volume 73, 2018, pp. 865–918, Arxiv

Web links

Individual evidence

  1. ↑ Dmitri Olegowitsch Orlow in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Entry at ncatlab
  3. ↑ Bondal-Orlov reconstruction theorem , ncatlab
personal data
SURNAME Orlov, Dmitri Olegowitsch
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH September 19, 1966
PLACE OF BIRTH Vladimir