Why Markman saves the Hodge conjecture for Weil type cycles from Kontsevich (in dimension 4)

by Patrick Brosnan (University of Maryland)

Wednesday 21 Jun 2023, 15:00 → 16:00 Europe/Rome

Aula Seminari (Department of Mathematics)

I'll explain two opposing pieces of work:  

(1) Markman's proof of the
Hodge conjecture for general Weil type abelian fourfolds of discriminant 1, and 

(2) Kontsevich's tropical approach to finding a counterexample to the Hodge
conjecture for Weil type abelian varieties.  

Then I'll explain why Markman's proof of the Hodge conjecture in the discriminant 1 case rules out Kontsevich's approach in dimension 4 (for arbitrary discriminant).