Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 11 (2018), 2039-2072.
Exceptional isogenies between reductions of pairs of elliptic curves
Let and be two elliptic curves over a number field. We prove that the reductions of and at a finite place are geometrically isogenous for infinitely many , and we draw consequences for the existence of supersingular primes. This result is an analogue for distributions of Frobenius traces of known results on the density of Noether–Lefschetz loci in Hodge theory. The proof relies on dynamical properties of the Hecke correspondences on the modular curve.
Duke Math. J., Volume 167, Number 11 (2018), 2039-2072.
Received: 26 August 2015
Revised: 8 February 2018
First available in Project Euclid: 26 June 2018
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Charles, François. Exceptional isogenies between reductions of pairs of elliptic curves. Duke Math. J. 167 (2018), no. 11, 2039--2072. doi:10.1215/00127094-2018-0011. https://projecteuclid.org/euclid.dmj/1530000176