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 conception, and mathematical physics. the idea that of the derived type of sheaves used to be invented by means of Grothendieck and Verdier within the Nineteen Sixties as a device to specific vital ends up in algebraic geometry equivalent to the duality theorem. within the Seventies, Beilinson, Gelfand, and Gelfand chanced on derived type of an algebraic sort will be comparable to that of a finite-dimensional non-commutative algebra, and Mukai stumbled on that there are non-isomorphic algebraic forms that experience identical derived different types. during this approach, the derived type offers 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 learn of derived different types. This e-book comprises the complaints of a convention held on the college of Tokyo in January 2011 at the present prestige of the learn on derived different types relating to algebraic geometry. such a lot articles are survey papers in this quickly constructing box. The publication is appropriate for mathematicians who are looking to input this intriguing box. a few easy wisdom of algebraic geometry is believed
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