Seminar

The Artin part of a motive, weights and motivic nearby sheaves

Algebro-Geometric and Homotopical Methods

02 March 11:00 - 12:00

Florian Ivorra - Université de Rennes 1

The notion of Artin part of a relative cohomological motive has been introduced by Ayoub and Zucker in their study of motives associated with compactifications of arithmetic quotients of Hermitian symmetric spaces. They predict the existence of a relation between the Artin part of relative motive and the (conjectural) punctual weight filtration on the heart of the (conjectural) motivic t-structure on the triangulated category of motives. In this talk, I will present a recent joint work with Julien Sebag in which verify the Hodge theoretic side of Ayoub-Zucker’s prediction for smooth cohomological motives. I will explain how to compute the Artin part of the motivic nearby sheaf and relate it to the Betti cohomology of Berkovich spaces defines by tubes in non-Archimedean geometry. In the first part of the lecture, I will explain the results about motivic nearby sheaves and their relation with tubes needed and obtained in a previous joint work with Ayoub and Sebag.
Organizers
Eric M. Friedlander
The University of Southern California
Lars Hesselholt
University of Copenhagen
Paul Arne Østvaer
University of Oslo

Program
Contact

Paul Arne Østvaer

paularne@math.uio.no

Other
information

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