Small heights in large non-Abelian extensions
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Small heights in large non-Abelian extensions. / Frey, Linda.
In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Vol. 23, No. 3, 2022, p. 1357-1393.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Small heights in large non-Abelian extensions
AU - Frey, Linda
N1 - Publisher Copyright: © 2022 Scuola Normale Superiore. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
U2 - 10.2422/2036-2145.201811_018
DO - 10.2422/2036-2145.201811_018
M3 - Journal article
AN - SCOPUS:85147985787
VL - 23
SP - 1357
EP - 1393
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
SN - 0391-173X
IS - 3
ER -
ID: 343341367