Seminario di Algebra

e Teoria dei Numeri 

del Dipartimento di Matematica dell'Università di Torino

Questa pagina registra l'attività del Seminario.

Pagina mantenuta da Andrea Mori

Prossimo Seminario


Giovedì 16 Gennaio 2025

Ore 11:30 -- Aula 5


Andrea Conti

(Un. Heidelberg)


Bogomolov property for Galois representations

with big local image


Abstract.  An algebraic extension of Q is said to have the Bogomolov property if the absolute logarithmic Weil height of its non-torsion elements is uniformly bounded from below. Given a continuous representation ρ of the absolute Galois group G_Q, one can ask whether the field fixed by ker(ρ) has the Bogomolov property (in short, we say that ρ has (B)). In a joint work with Lea Terracini, we prove that, if ρ : G_Q--->GL_N(Z_p) maps an inertia subgroup at p surjectively onto an open subgroup of GL_N(Z_p), then ρ has (B). More generally, we show that if the image of a decomposition group at $p$ is open in the image of G_Q, and a certain condition on the center of the image is satisfied, then ρ has (B). In particular, no assumption on the modularity of ρ is needed, contrary to previous work of Habegger and Amoroso—Terracini.


 


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