# Derived Categories in Algebraic Geometry—Tokyo 2011

Share this page *Edited by *
*Yujiro Kawamata*

A publication of the European Mathematical Society

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 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 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.

#### Readership

Graduate students and research mathematicians interested in derived categories in algebraic geometry.