Algebraic and Arithmetic Geometry Seminar
# Why Markman saves the Hodge conjecture for Weil type cycles from Kontsevich (in dimension 4)

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Europe/Rome

Aula Seminari (Department of Mathematics)
### Aula Seminari

#### Department of Mathematics

Description

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).