5 citations · 14 across the 11 of their papers we have counts for
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Mumford-Tate groups of 1-motives and Weil pairing
Cristiana Bertolin, Patrice Philippon
We show how the geometry of a 1-motive (that is existence of endomorphisms and relations between the points defining it) determines the dimension of its motivic Galois group ${…
Arithmetic positivity on toric varieties
Jose Ignacio Burgos Gil, Atsushi Moriwaki, Patrice Philippon +1
We continue with our study of the arithmetic geometry of toric varieties. In this text, we study the positivity properties of metrized R-divisors in the toric setting. For a toric…
Arithmetic geometry of toric varieties. Metrics, measures and heights
José Ignacio Burgos Gil, Patrice Philippon, Martín Sombra
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave funct…
A refinement of the Kushnirenko-Bernstein estimate
Patrice Philippon, Martin Sombra
A theorem of Kushnirenko and Bernstein shows that the number of isolated roots of a system of polynomials in a torus is bounded above by the mixed volume of the Newton polytopes of…
Diophantine geometry and toric varieties
Patrice Philippon, Martin Sombra
We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometric…