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.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze |
Vol/bind | 23 |
Udgave nummer | 3 |
Sider (fra-til) | 1357-1393 |
Antal sider | 37 |
ISSN | 0391-173X |
DOI | |
Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
This research was done during my PhD at Universität Basel in the DFG project 223746744 “Heights and unlikely intersections” and written up during my SNF grant Early.PostDoc Mobility at the University of Copenhagen. Received November 23, 2018; accepted in revised form April 22, 2021. Published online September 2022.
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