2020/09/10 by Ryota Mikami, Mikami, Ryota · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2009.04677
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.