Small heights in large non-Abelian extensions

Department of Mathematical Sciences

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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

Harvard

Frey, L 2022, 'Small heights in large non-Abelian extensions', Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 23, no. 3, pp. 1357-1393. https://doi.org/10.2422/2036-2145.201811_018

APA

Frey, L. (2022). Small heights in large non-Abelian extensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 23(3), 1357-1393. https://doi.org/10.2422/2036-2145.201811_018

Vancouver

Frey L. Small heights in large non-Abelian extensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2022;23(3):1357-1393. https://doi.org/10.2422/2036-2145.201811_018

Author

Frey, Linda. / Small heights in large non-Abelian extensions. In: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2022 ; Vol. 23, No. 3. pp. 1357-1393.

Bibtex

@article{2bf7010a6ca740e385551f0ca866bcff,

title = "Small heights in large non-Abelian extensions",

abstract = "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.",

author = "Linda Frey",

year = "2022",

doi = "10.2422/2036-2145.201811_018",

language = "English",

volume = "23",

pages = "1357--1393",

journal = "Annali della Scuola Normale Superiore di Pisa - Classe di Scienze",

issn = "0391-173X",

publisher = "Scuola Normale Superiore - Edizioni della Normale",

number = "3",

}

RIS

TY - JOUR

T1 - Small heights in large non-Abelian extensions

AU - Frey, Linda

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