1 citations · 2 across the 8 of their papers we have counts for
8 papers
Tropical cohomology via reductions of tropical varieties
Ryota Mikami
Itenberg-Katzarkov-Mikhalkin-Zharkov gave an isomorphism of tropical cohomology and cohomology of some maximally degenerate algebraic varieties. Their proof was based on tropical a…
Tropical intersection homology
Ryota Mikami
Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivale…
On tropical Hodge theory for tropical varieties
Ryota Mikami
To prove log-concavity of the characteristic polynomials of matroids, Adiprasito-Huh-Katz proved the Kähler package (the hard Lefschetz theorem and the Hodge-Riemann bilinear relat…
Differential forms and cohomology in tropical and complex geometry
Ryota Mikami
Ducros, Hrushovski, and Loeser gave maps from families of archimedean diffrential forms to non-archiemedean (or tropical) ones, which are compatible with integrals on algebraic var…
On tropical cohomology of smooth algebraic varieties
Ryota Mikami
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 se…
Tropical analogs of Milnor -groups and tropicalizations of Zariski-Riemann spaces
Ryota Mikami
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) Mi…
A tropical characterization of algebraic subvarieties of toric varieties over non-archimedean fields
Ryota Mikami
We study the tropicalizations of analytic subvarieties of normal toric varieties over complete non-archimedean valuation fields. We show that a Zariski closed analytic subvariety o…
Cyclic coverings of the projective line by Mumford curves in positive characteristic
Ryota Mikami
We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of a cyclic covering of degree of the projective line by a M…