By Yujiro Kawamata

ISBN-10: 3037191155

ISBN-13: 9783037191156

The examine of derived different types is a topic that draws more and more many mathematicians from quite a few fields of arithmetic, together with summary algebra, algebraic geometry, illustration concept, and mathematical physics. the idea that of the derived type of sheaves used to be invented by way of Grothendieck and Verdier within the Sixties as a device to precise very important leads to algebraic geometry akin to the duality theorem. within the Nineteen Seventies, Beilinson, Gelfand, and Gelfand came across derived class of an algebraic sort might be similar to that of a finite-dimensional non-commutative algebra, and Mukai stumbled on that there are non-isomorphic algebraic kinds that experience identical derived different types. during this manner, the derived type offers 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 reflect symmetry supplied additional motivation for the examine of derived different types. This ebook comprises the court cases 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. so much articles are survey papers in this swiftly constructing box. The ebook is acceptable for mathematicians who are looking to input this interesting box. a few simple wisdom of algebraic geometry is believed

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**Extra info for Derived Categories in Algebraic Geometry: Tokyo 2011**

**Example text**

15. (i) Notice that in [16] a more general result is proved. In particular, the target category can be any triangulated category while the source category can be the category of perfect (supported) complexes on a noetherian scheme. (ii) One may easily extend the proof above to the case of twisted varieties. 5 of [9]. We leave this to the reader. 4 The (partial) answers to (Q2)–(Q5) We postpone for the moment the discussion about (Q1) which will be examined in Section 5. The remaining problems can be studied in a unitary way explained here below.

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10, 1406–13. [13] M. Bernardara and M. Bolognesi, Derived categories and rationality of conic bundles. AG]. [14] M. Bernardara, E. Macrì, S. Mehrotra, and P. Stellari, A categorical invariant for cubic threefolds. Adv. Math. 229 (2012), no. 2, 770–803. [15] S. Bloch and J. P. Murre, On the Chow group of certain types of Fano threefolds. Compositio Math. 39 (1979), no. 1, 47–105. [16] A. I. Bondal, Representations of associative algebras and coherent sheaves. Math. USSR Izv. 34 (1990), no. 1, 23–42.

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Categories: Algebraic Geometry