On Secondary Invariants and Arithmetic Rigidity

Apr 23, 2024, 11:00 AM
1h
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

Speaker

Prof. Dustin Clausen (IHES)

Description

A complex local system on a space $S$ gives rise to "secondary" Chern classes in $H^{2p-1}(S; \mathbb{C}/\mathbb{Z}(p))$, refining the usual "primary" Chern classes in $H^{2p}(S;\mathbb{Z}(p))$. In fact, Esnault in a survey article describes four methods of defining such classes, of which 3 are proved to be equivalent by means of her "modified splitting principle". I will explain how to show that the remaining 1 out of 4 definitions, that of Cheeger-Simons, agrees with the others. Then, changing gears, I will describe some arithmetic analogs of the phenomenon of rigidity of secondary Chern classes. This has bearing on another question from Esnault's article, and leads us to some motivic speculations.

Presentation materials