Olivier Benoist
(ENS, CNRS)

10/25/22, 9:00 AM

The first counterexamples to the integral Hodge conjecture,

due to Atiyah and Hirzebruch, exploit the action of Steenrod operations.

In this talk, we will further study the interaction of Steenrod

operations and algebraic classes, over arbitrary fields, and we will

derive new examples of non-algebraic cohomology classes.

Claire Voisin
(CNRS, IMJ-PRG)

10/25/22, 10:15 AM

We prove that for any rationally connected threefold X over the complex numbers, there exists a smooth projective surface S and a family of 1-cycles on X parameterized by S, inducing an Abel-Jacobi isomorphism Alb(S)≅J^3(X). This statement was previously known for some classes of smooth Fano threefolds.