Seminar des SFB/TRR 326 GAUS Bogomolov property for Galois representations with big local image
- Freitag, 27. Juni 2025, 13:30 - 14:30 Uhr
- INF 205, SR A
- Dr. Andreas Conti
Adresse
INF 205, SR A
Livestream
Veranstalter
Prof. G. Böckle
Veranstaltungstyp
Vortrag
An algebraic extension of the rational numbers 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 Gℚ of 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: Gℚ → GLN(ℤp) maps an inertia subgroup at p surjectively onto an open subgroup of GLN(ℤp), then ρ has (B). More generally, we show that if the image of a decomposition group at p is open in the image of Gℚ, plus 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.