Vol. 301, No. 1, 2019

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Lifting of Elliptic curves

Sanoli Gun and V. Kumar Murty

Vol. 301 (2019), No. 1, 101–106
DOI: 10.2140/pjm.2019.301.101
Abstract

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

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