Mathematics – K-Theory and Homology
Scientific paper
2005-07-11
Mathematics
K-Theory and Homology
26 pages, in French with an introduction in English
Scientific paper
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.
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