By Yujiro Kawamata

The examine of derived different types is a topic that pulls more and more many mathematicians from quite a few fields of arithmetic, together with summary algebra, algebraic geometry, illustration concept, and mathematical physics. the concept that of the derived class of sheaves used to be invented via Grothendieck and Verdier within the Nineteen Sixties as a device to specific very important leads to algebraic geometry similar to the duality theorem. within the Nineteen Seventies, Beilinson, Gelfand, and Gelfand came across derived class of an algebraic style can be comparable to that of a finite-dimensional non-commutative algebra, and Mukai chanced on that there are non-isomorphic algebraic forms that experience similar derived different types. during this approach, the derived class presents a brand new idea that has many incarnations. within the Nineties, Bondal and Orlov exposed an unforeseen parallelism among the derived different types and the birational geometry. Kontsevich's homological replicate symmetry supplied extra motivation for the research of derived different types. This e-book comprises the complaints of a convention held on the collage of Tokyo in January 2011 at the present prestige of the learn on derived different types concerning algebraic geometry. so much articles are survey papers in this swiftly constructing box. The ebook is appropriate for mathematicians who are looking to input this fascinating box. a few uncomplicated wisdom of algebraic geometry is believed

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