Small heights in large non-Abelian extensions
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Let E be an elliptic curve over the rationals. Let L be an infinite Galois extension of the rationals with uniformly bounded local degrees at almost all primes. We will consider the infinite extension L(Etor) of the rationals which is generated by the set of x- and y-coordinates of the torsion points in E with respect to a Weierstrass model of E with rational coefficients. In this paper we will prove a lower bound for the absolute logarithmic Weil height of non-zero elements in L(Etor) that are not a root of unity.
Original language | English |
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Journal | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze |
Volume | 23 |
Issue number | 3 |
Pages (from-to) | 1357-1393 |
Number of pages | 37 |
ISSN | 0391-173X |
DOIs | |
Publication status | Published - 2022 |
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