Motives, quadratic forms and arithmetic

Session

Tuesday Morning

Oct 25, 2022, 9:00 AM

Louvre Lens Vallée

2. Steenrod operations and algebraic classes

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.

5. Geometric representability of 1-cycles on rationally connected threefolds

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.

3. The Picard-Lefschetz formula for normal crossings

Moritz Kerz

10/25/22, 11:30 AM

In the study of semi-stable degeneration of Lefschetz pencils one is led to a generalization of the classical Picard-Lefschetz formula for certain perverse sheaves on normal crossing spaces. In the talk I will recall the formalism of nearby cycle and vanishing cycle functors and I will explain how Hodge theory allows one to obtain the normal crossing Picard-Lefschetz formula.
Joint work with...