Hardcover ISBN:  9783037191156 
Product Code:  EMSSCR/8 
List Price:  $98.00 
AMS Member Price:  $78.40 
Hardcover ISBN:  9783037191156 
Product Code:  EMSSCR/8 
List Price:  $98.00 
AMS Member Price:  $78.40 

Book DetailsEMS Series of Congress ReportsVolume: 8; 2012; 354 ppMSC: Primary 13; 14; 16; 18;
The study of derived categories is a subject that attracts increasingly many 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 finitedimensional noncommutative algebra, and Mukai found that there are nonisomorphic 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 the derived categories and the birational geometry. Kontsevich's homological mirror symmetry provided further motivation for the study of derived categories.
This book contains 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 mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
ReadershipGraduate students and research mathematicians interested in derived categories in algebraic geometry.

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The study of derived categories is a subject that attracts increasingly many 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 finitedimensional noncommutative algebra, and Mukai found that there are nonisomorphic 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 the derived categories and the birational geometry. Kontsevich's homological mirror symmetry provided further motivation for the study of derived categories.
This book contains 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 mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Graduate students and research mathematicians interested in derived categories in algebraic geometry.