Algebraic Topology Seminar

Monday, January 29, 2024 at 4:30pm to 6:00pm

Building 2, 131
182 MEMORIAL DR, Cambridge, MA 02139

Speaker:  Alexander Efimov (Steklov Mathematical Institute of Russian Academy of Sciences and National Research University Higher School of Economics)

Title:  Localizing motives and corepresentability of TR and TC

Abstract:  I will explain some of my recent results on the category of localizing
motives – the target of the universal localizing invariant commuting with
filtered colimits. The main surprising result about this category is that it
is rigid as a symmetric monoidal category (in the sense of Gaitsgory and

As an application of the proof of rigidity, we will deduce that the func-
tors TR (topological restriction) and TC (topological cyclic homology) are
corepresentable in this category, if we restrict to connective E- rings. If time permits, I will explain how rigidity of M otl oc allows to con-
struct refined versions of (topological) Hochschild homology and its vari-
ants, which contain much more information about the E1 − algebra than
the usual variants of (T)HH.





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