Tropical Analog of the Hodge Conjecture for Smooth Algebraic Varieties Over Trivially Valued Fields

Explore a lecture on the tropical analog of the Hodge conjecture for smooth algebraic varieties over trivially valued fields, presented by Ryota Mikami from Kyoto University. Delve into the world of tropical geometry as a combinatorial shadow of algebraic geometry, and discover a novel approach to problems on cycle class maps. Learn about the main components of the proof, including a theorem for general "cohomology theories" developed by mathematicians like Quillen, a newly introduced tropical analog of Milnor K-theory, and explicit calculations of tropical cohomology of trivial line bundles using non-archimedean geometry. Gain insights into this complex mathematical topic and its implications for the field of algebraic geometry during this hour-long presentation.