Etale motivic cohomology of some Fano fivefolds.

par Ivan Rosas-Soto

jeudi 7 mai 2026, 14:00 → 15:00 Europe/Paris

M7-411 (UMPA)

In this talk, I will review the Chow and étale motivic cohomology groups of smooth, complete intersections with Hodge structures of level one, as classified by Deligne and Rapoport. I will pay particular attention to fivefolds and explain how the comparison map between Chow and étale motivic cohomology interacts with the birational properties of such varieties. I will show how these results can be extended to algebraic cycles on other smooth Fano manifolds with Hodge structures of level one. Finally, I will present some preliminary results regarding the comparison map for certain Fano manifolds of Calabi–Yau type, focusing particularly on double quartic fivefolds. I will pay special attention to their unramified cohomology groups with torsion coefficients and the integral Hodge conjecture. These results are based on ongoing work with Pedro Montero.