Speaker: Pavel Sechin
Affiliation: University of Regensburg, Germany
Title of Talk: Descent of motives along function field extensions
Date: March 27, 2026
Time: 11:00:00 Hours
Venue: A-369

Abstract: I will address the following question: given a motive over a smooth projective variety X over k, when does it come from a motive over k? It turns out that whenever X is `isotropic' with respect to the cohomology theory, there is a full answer to this question. Moreover, under some further assumptions on the motive, one can solve a stronger problem: descent of a motive over k(X) to k. The solution is the key step in constructing motives corresponding to the Galois cohomology with finite coefficients. If time permits, I will explain how this gives a potentially working strategy to attack the Kahn--Rost--Sujatha conjecture on the unramified cohomology of quadrics.