Tropical analogs of Milnor $K$-groups and tropicalizations of Zariski-Riemann spaces

Abstract

As a step of a tropical approach to problems on algebraic classes of cohomology groups (such as the Hodge conjecture), in this paper, we introduce tropical analogs of (rational) Milnor $K$-groups, and prove the existence of the Gersten resolution of their Zariski sheafification. Our result will be used to prove a tropical analog of the Hodge conjecture for smooth algebraic varieties over trivially valued fields in a subsequent paper.

This paper was withdrawn because the content of this paper was largely fixed and the new version is now contained in another paper arXiv:2009.04690.v5. Please refer to that paper instead of this old paper

Cited by in corpus (1)

• Homology of tropical fans