JournalsjemsVol. 24, No. 9pp. 3161–3182

Independence of CM points in elliptic curves

  • Jonathan Pila

    Oxford University, UK
  • Jacob Tsimerman

    University of Toronto, Canada
Independence of CM points in elliptic curves cover
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Abstract

We prove a result which describes, for each n1n \geq 1, all linear dependencies among nn images in a given elliptic curve of special points in a given modular or Shimura curve under a given parameterization (or correspondence). Our result unifies and improves in certain aspects previous work of Rosen–Silverman–Kühne and Buium–Poonen.

Cite this article

Jonathan Pila, Jacob Tsimerman, Independence of CM points in elliptic curves. J. Eur. Math. Soc. 24 (2022), no. 9, pp. 3161–3182

DOI 10.4171/JEMS/1161