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math.NT2016
On the essential minimum of Faltings' height
José Burgos Gil, Ricardo Menares, Juan Rivera-Letelier
We study the essential minimum of the (stable) Faltings height on the moduli space of elliptic curves. We prove that, in contrast to the Weil height on a projective space and the N…
math.NT2016
Strong modularity of reducible Galois representations
Nicolas Billerey, Ricardo Menares
In this paper, we call strongly modular those reducible semi-simple odd mod Galois representations for which the conclusion of the strongest form of Serre's original modularity…