Vortrag
On the algebraicity of de Rham-Betti classes for products of elliptic curves
Vortrag von Prof. Dr. Charles Vial
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 21.11.22 Zeit: 13.15 - 14.45 Raum: Y27H25
A de Rham-Betti class on a smooth projective variety X over a number field K is a rational class in the Betti cohomology of the analytification of X that descends to a class in the algebraic de Rham cohomology of X via the period comparison isomorphism. These classes are the analogues of Hodge classes, except that one uses the K-structure on de Rham cohomology instead of the Hodge filtration. The period conjecture of Grothendieck implies that de Rham–Betti classes should be algebraic. I will report on joint work with Mingmin Shen, where we prove that any de Rham–Betti class on a product of elliptic curves is algebraic. As a key intermediate step in the proof, we show that certain codimension-2 de Rham-Betti classes on hyper-Kähler varieties are Hodge.