Lifting of Elliptic curves

Suppose that for all but finitely many primes $p$ we are given an elliptic curve $E_{p}$ defined over a finite field $F_{p}$ of $p$ elements. We derive a criterion for there to exist an elliptic curve $E$ defined over $ℚ$ for which the reduction of $E$ modulo $p$ is isogenous to $E_{p}$ for almost all $p$ .

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Keywords

lifting of elliptic curves, Chebotarev density theorem, generalized Riemann hypothesis, $\ell$-adic representations attached to elliptic curves

Mathematical Subject Classification 2010

Primary: 11F11, 11G05

Milestones

Received: 9 November 2018

Accepted: 6 April 2019

Published: 16 September 2019

Authors

Sanoli Gun
The Institute of Mathematical Sciences HBNI C.I.T Campus, Taramani Chennai India

V. Kumar Murty
Department of Mathematics University of Toronto Toronto, ON Canada

Vol. 301, No. 1, 2019

Sanoli Gun and V. Kumar Murty

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors