Tropical geometry is a combinatorial shadow of algebraic geometry and has many applications. We propose a tropical approach to problems on cycle class maps, in particular, the Hodge conjecture. In this talk, I would like to explain a proof of a tropical analog of the Hodge conjecture for smooth algebraic varieties over the field of complex numbers (or trivially valued fields). The main ingredients are an algebro-geometric theorem of cohomology theories (exactness of the Gersten resolutions), which is developped by many mathematicians, and non-archimedean geometry.
This is a zoom seminar.