Effective Kummer Theory for Elliptic Curves

Reference : Effective Kummer Theory for Elliptic Curves


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/43271

Title :	Effective Kummer Theory for Elliptic Curves
Language :	English
Author, co-author :	Lombardo, Davide [Università di Pisa > Dipartimento di Matematica]
	Tronto, Sebastiano [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	Undated
Peer reviewed :	No
Keywords :	[en] Elliptic curves ; Kummer Theory
Abstract :	[en] Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])]. When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality [Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α.
Permalink :	http://hdl.handle.net/10993/43271
source URL :	https://arxiv.org/abs/1909.05376

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