03690nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002900185245010100214260008200315300003400397336002600431337002600457338003600483347002400519490005400543505096900597506006601566520141401632650003103046650002803077650004003105650004003145700003103185856003203216856006803248161-130107CH-001817-320130107234500.0a fot ||| 0|cr nn mmmmamaa130107e20130107sz fot ||| 0|eng d a978303719615170a10.4171/1152doi ach0018173 7aPBMW2bicssc a14-xxa13-xxa16-xx2msc10aDerived Categories in Algebraic Geometryh[electronic resource] :bTokyo 2011 /cYujiro Kawamata3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (354 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Congress Reports (ECR) ;x2523-515X00tCategorical representability and intermediate Jacobians of Fano threefolds /rMarcello Bernardara, Michele Bolognesi --tFourier–Mukai functors: a survey /rAlberto Canonaco, Paolo Stellari --tFlops and about: a guide /rSabin Cautis --tA note on derived categories of Fermat varieties /rAkira Ishii, Kazushi Ueda --tHomology of infinite loop spaces /rDmitry Kaledin --tCluster algebras and derived categories /rBernhard Keller --tSome derived equivalences between noncommutative schemes and algebras /rIzuru Mori --tLagrangian-invariant sheaves and functors for abelian varieties /rAlexander Polishchuk --tGeneric vanishing filtrations and perverse objects in derived categories of coherent sheaves /rMihnea Popa --tThe fundamental group is not a derived invariant /rChristian Schnell --tIntroduction and open problems of Donaldson–Thomas theory /rYukinobu Toda --tNotes on formal deformations of abelian categories /rMichel Van den Bergh.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe study of derived categories is a subject that attracts increasingly many young 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 derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories.
This book is 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 young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aCommutative rings and algebras2msc07aAssociative rings and algebras2msc1 aKawamata, Yujiro,eeditor.40uhttps://doi.org/10.4171/115423cover imageuhttps://www.ems-ph.org/img/books/kawamata_mini.jpg