2005/07/11 by Goncalo Tabuada, Tabuada, Goncalo
Mathematics · #16E45 (Primary) 18E30 #18E35 (Secondary) #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #math.KT #math.RT #msc:16E45 #msc:18E30 #msc:18E35
paper · pdf · doi:10.48550/arxiv.math/0507227
26 pages, in French with an introduction in English
arxiv created 2005/07/11 · arxiv updated 2009/12/01
With the help of the tools of Quillen's homotopical algebra, we construct `the universal additive invariant', namely a functor from the category of small dg categories to an additive category, that inverts the Morita dg functors, transforms the semi-orthogonal decompositions in the sense of Bondal-Orlov into direct sums and which is universal for these properties. We compare our construction with that of Bondal-Larsen-Lunts. ----- A l'aide des outils de l'algebre homotopique de Quillen, on construit `l'invariant additif universel', c'est-a-dire un foncteur defini sur la categorie des petites dg-categories et a valeurs dans une categorie additive qui rend inversibles les dg-foncteurs de Morita, transforme les decompositions semi-orthogonales au sens de Bondal-Orlov en sommes directes et qui est universel pour ces proprietees. Nous comparons notre construction a celle de Bondal-Larsen-Lunts.