11 citations · 14 across the 4 of their papers we have counts for
5 papers
Tropical Feichtner-Yuzvinsky and positivity criterion for fans
Omid Amini, Matthieu Piquerez
We prove that the Chow ring of any simplicial fan is isomorphic to the middle degree part of the tropical cohomology ring of its canonical compactification. Using this result, we p…
A First Order Theory of Diagram Chasing
Assia Mahboubi, Matthieu Piquerez
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chas…
Homology of tropical fans
Omid Amini, Matthieu Piquerez
The aim of this paper is to study homological properties of tropical fans and to propose a notion of smoothness in tropical geometry, which goes beyond matroids and their Bergman f…
Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class
Omid Amini, Matthieu Piquerez
This is a sequel to our work in tropical Hodge theory. Our aim here is to prove a tropical analogue of the Clemens-Schmid exact sequence in asymptotic Hodge theory. As an applicati…
Hodge theory for tropical varieties
Omid Amini, Matthieu Piquerez
In this paper we prove that the cohomology of smooth projective tropical varieties verify the tropical analogs of three fundamental theorems which govern the cohomology of complex…