Triangulated categories, weight structures, and weight complexes

• 主讲人：Mikhail Bondarko (St. Petersburg State University)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2022-09-22 21:00 - 2022-09-22 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/2C3167F7FADFEB83417F8A3A80B9527E
Valid Until: 2026-10-31 23:59

 

Abstract: (Co)homology functors usually yield certain functors into triangulated categories. I will justify this claim and recall some basics on homotopy categories of complexes and other triangulated categories. Next, I define weight structures on triangulated categories; these were independently introduced by B. and D. Pauksztello. Weight structures give certain filtrations of triangulated categories; the definition is a certain cousin of that of t-structures. I will mention some methods of constructing weight structures as well as interesting "topological" and motivic examples. Weight structures give certain weight complex functors that are "usually" exact; they are also conservative up to "objects of infinitely large and infinitely small weights" (that is, weight complexes only kill extensions of objects of these two sorts). In particular, one has an exact conservative functor from geometric Voevodsky motives into complexes of Chow motives, whereas the corresponding weight spectral sequences vastly generalize Deligne’s ones. Weight complexes also enable one to calculate the corresponding pure functors; some of the latter are quite new and interesting.

The talk can be interesting to anyone who had some experience with (co)homology and categories.

 

Bio: Mikhail Bondarko is an associate professor at the St. Petersburg State University and also a professor of the Russian Academy of Sciences. He obtained his PhD in 2000 and got his Doctor Degree (habilitation) in 2007. He has some prestigious awards; this includes first prize in the Chinese Mathematical Olympiad in 1994. Currently, Bondarko studies triangulated categories (including motivic ones), weight structures, and t-structures on them. He also has several papers on formal groups, finite flat group schemes, and additive Galois modules.