Séminaire de Mathématique

Weight Structures on Triangulated Categories

by Prof. Mikhail Bondarko (St. Petersburg State University & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Weight structures give certain filtrations of triangulated categories; the definition is a certain cousin of that of  t-structures. Particular cases of weight decompositions give stupid filtrations of complexes and cellular towers for spectra.  I will also mention interesting motivic and Hodge-theoretic examples of weight structures along with methods for constructing them. Weight structures yield weight filtrations and spectral sequences for cohomology as well as certain weight complex functors. In particular,  there exists an exact conservative functor from (relative) constructible Voevodsky motives into complexes of Chow motives, whereas the corresponding weight spectral sequences vastly generalize Deligne's ones. Lastly, the relations between weight structures and t-structures yield new methods for constructing t-structures and proving their properties.

Organized by

Maxim Kontsevich