How big is the image of the Galois representations attached to CM elliptic curves?

Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Aufsatz in Konferenzband › Forschung › Peer-Review

Autoren

  • Francesco Campagna
  • Riccardo Pengo

Externe Organisationen

  • Max-Planck-Institut für Mathematik
  • École normale supérieure de Lyon (ENS de Lyon)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Titel des SammelwerksArithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021
Herausgeber/-innenSamuele Anni, Valentijn Karemaker, Elisa Lorenzo García
Herausgeber (Verlag)American Mathematical Society
Seiten41-56
Seitenumfang16
ISBN (Print)9781470467944
PublikationsstatusVeröffentlicht - 2022
Extern publiziertJa
Veranstaltung18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021 - Virtual, Online
Dauer: 31 Mai 2021 → 4 Juni 2021

Publikationsreihe

NameContemporary Mathematics
Band779
ISSN (Print)0271-4132
ISSN (elektronisch)1098-3627

Abstract

Using an analogue of Serre’s open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve E defined over a number field F a natural number I(E/F) which describes how big the image of the Galois representation associated to E is. We show how one can compute I(E/F), using a closed formula that we obtain from the classical theory of complex multiplication.

ASJC Scopus Sachgebiete

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How big is the image of the Galois representations attached to CM elliptic curves? / Campagna, Francesco; Pengo, Riccardo.
Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Hrsg. / Samuele Anni; Valentijn Karemaker; Elisa Lorenzo García. American Mathematical Society, 2022. S. 41-56 (Contemporary Mathematics; Band 779).

Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Aufsatz in Konferenzband › Forschung › Peer-Review

Campagna, F & Pengo, R 2022, How big is the image of the Galois representations attached to CM elliptic curves? in S Anni, V Karemaker & EL García (Hrsg.), Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Contemporary Mathematics, Bd. 779, American Mathematical Society, S. 41-56, 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, AGC2T 2021, Virtual, Online, 31 Mai 2021. https://doi.org/10.1090/conm/779/15670
Campagna, F., & Pengo, R. (2022). How big is the image of the Galois representations attached to CM elliptic curves? In S. Anni, V. Karemaker, & E. L. García (Hrsg.), Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021 (S. 41-56). (Contemporary Mathematics; Band 779). American Mathematical Society. https://doi.org/10.1090/conm/779/15670
Campagna F, Pengo R. How big is the image of the Galois representations attached to CM elliptic curves? in Anni S, Karemaker V, García EL, Hrsg., Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. American Mathematical Society. 2022. S. 41-56. (Contemporary Mathematics). doi: 10.1090/conm/779/15670
Campagna, Francesco ; Pengo, Riccardo. / How big is the image of the Galois representations attached to CM elliptic curves?. Arithmetic, Geometry, Cryptography, and Coding Theory - 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, 2021. Hrsg. / Samuele Anni ; Valentijn Karemaker ; Elisa Lorenzo García. American Mathematical Society, 2022. S. 41-56 (Contemporary Mathematics).
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