Tropical cohomology via reductions of tropical varieties

Abstract

Itenberg-Katzarkov-Mikhalkin-Zharkov gave an isomorphism of tropical cohomology and cohomology of some maximally degenerate algebraic varieties. Their proof was based on tropical analogs of Steenbrink's geometric monodromy-weight spectral sequences. These were generalized to the non-realizable case by Amini-Piquerez. In this paper, we give a new construction of these tropical spectral sequences in the same way as Steenbrink's ones. For this purpose, we introduce reductions of tropical varieties. We also show that eigenwave actions are given by tropical Gauss-Manin connections.