11 citations · 18 across the 9 of their papers we have counts for
10 papers
Homological smoothness and Deligne resolution for tropical fans
Omid Amini, Matthieu Piquerez
We say that a tropical fan is homologically smooth if each of its open subsets verify tropical Poincare duality. A tropical homology manifold is a tropical variety that is locally…
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…
Machine-Checked Categorical Diagrammatic Reasoning
Benoît Guillemet, Assia Mahboubi, Matthieu Piquerez
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This librar…
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…
Hodge theory for tropical fans
Omid Amini, Matthieu Piquerez
This paper is the first in a series devoted to the development of a Hodge theory for tropical varieties. We introduce a notion of T-stability for tropical fans and prove that vario…
Cohomologically tropical varieties
Edvard Aksnes, Omid Amini, Matthieu Piquerez +1
Given the tropicalization of a complex subvariety of the torus, we define a morphism between the tropical cohomology and the rational cohomology of their respective tropical compac…
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…
A multidimensional generalization of Symanzik polynomials
Matthieu Piquerez
Symanzik polynomials are defined on Feynman graphs and they are used in quantum field theory to compute Feynman amplitudes. They also appear in mathematics from different perspecti…