English

On tropical cohomology of smooth algebraic varieties

Algebraic Geometry 2025-07-23 v6

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.

Keywords

Cite

@article{arxiv.2009.04690,
  title  = {On tropical cohomology of smooth algebraic varieties},
  author = {Ryota Mikami},
  journal= {arXiv preprint arXiv:2009.04690},
  year   = {2025}
}

Comments

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,