Bogomolov property of some infinite nonabelian extensions of a totally -adic field
Tom 213 / 2024
Streszczenie
Let E be an elliptic curve defined over a number field K, and let v be a finite place of K. Write K^{tv} for the maximal totally v-adic field, and denote by L the field generated over K^{tv} by all torsion points of E. Under some conditions, we will show that the absolute logarithmic Weil height (resp. Néron–Tate height) of any element of L (resp. E(L)) is either 0 or bounded from below by a positive constant depending only on E,K and v. This constant will be explicit in the toric case.