By Yujiro Kawamata

The examine of derived different types is a topic that pulls more and more many mathematicians from a variety of fields of arithmetic, together with summary algebra, algebraic geometry, illustration idea, and mathematical physics. the concept that of the derived type of sheaves was once invented via Grothendieck and Verdier within the Nineteen Sixties as a device to specific very important leads to algebraic geometry resembling the duality theorem. within the Nineteen Seventies, Beilinson, Gelfand, and Gelfand came across derived classification of an algebraic sort should be such as that of a finite-dimensional non-commutative algebra, and Mukai chanced on that there are non-isomorphic algebraic forms that experience identical derived different types. during this method, the derived type presents a brand new idea that has many incarnations. within the Nineteen Nineties, Bondal and Orlov exposed an unforeseen parallelism among the derived different types and the birational geometry. Kontsevich's homological replicate symmetry supplied additional motivation for the examine of derived different types. This e-book includes the complaints of a convention held on the collage of Tokyo in January 2011 at the present prestige of the examine on derived different types on the topic of algebraic geometry. so much articles are survey papers in this speedily constructing box. The booklet is appropriate for mathematicians who are looking to input this intriguing box. a few simple wisdom of algebraic geometry is thought

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