On tropical cohomology of smooth algebraic varieties

Abstract

In this paper, we give an explicit description of tropical cohomology of smooth algebraic varieties over trivially valued fields. We also construct ``monodromy weight'' spectral sequences for tropical cohomology of geometric strictly semi-stable reductions.

60 pages. version 6 largely changed. Proof was simplified. The case of semi-stable reduction was added. Title changed from "On tropical cycle class maps", version 5: largely changed. Title changed from "A tropical analog of the Hodge conjecture for smooth algebraic varieties over trivially valued fields". This paper contains the contents of arXiv: 2009.04677, version2, 3, 4:minor changes,

References in corpus (4)

• Hodge theory for tropical varieties
• Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class
• Homology of tropical fans
• Tropical Abelian varieties, Weil classes and the Hodge Conjecture

Cited by in corpus (1)

• Homology of tropical fans