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Field name	Details
Title	Derived Categories in Algebraic Geometry ([EBook] :) : Tokyo 2011 / / Yujiro Kawamata
Added Personal Name	Kawamata, Yujiro
Publication	Zuerich, Switzerland : : European Mathematical Society Publishing House, , 2013
Physical Details	1 online resource (354 pages)
Series	EMS Series of Congress Reports (ECR) 2523-515X
ISBN	9783037196151
Summary Note	The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories. This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.:
Contents note	Categorical representability and intermediate Jacobians of Fano threefolds /: Fourier–Mukai functors: a survey /: Flops and about: a guide /: A note on derived categories of Fermat varieties /: Homology of infinite loop spaces /: Cluster algebras and derived categories /: Some derived equivalences between noncommutative schemes and algebras /: Lagrangian-invariant sheaves and functors for abelian varieties /: Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves /: The fundamental group is not a derived invariant /: Introduction and open problems of Donaldson–Thomas theory /: Notes on formal deformations of abelian categories /:
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.4171/115
See Also	https://www.ems-ph.org/img/books/kawamata_mini.jpg
Links to Related Works	Subject References: Algebraic Geometry . Associative Rings and Algebras . Commutative Rings and Algebras . Authors: editor . Kawamata, Yujiro . Series: EMS Series of Congress Reports (ECR) .

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Derived Categories in Algebraic Geometry: Tokyo 2011 /

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