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Chapitre D'ouvrage Année : 2021

On Sato-Tate distributions, extremal traces, and real multiplication in genus 2

David Kohel
Yih-Dar Shieh
  • Fonction : Auteur

Résumé

The vertical Sato-Tate conjectures gives expected trace distributions for for families of curves. We develop exact expression for the distribution associated to degree-4 representations of USp(4), SU(2) × SU(2) and SU(2) in the neighborhood of the extremities of the Weil bound. As a consequence we derive qualitative distinctions between the extremal traces arising from generic genus-2 curves and genus-2 curves with real or quaternionic multiplication. In particular we show, in a specific sense, to what extent curves with real multiplication dominate the contribution to extremal traces.
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Dates et versions

hal-03089551 , version 1 (28-12-2020)

Identifiants

Citer

David Kohel, Yih-Dar Shieh. On Sato-Tate distributions, extremal traces, and real multiplication in genus 2. Stéphane Ballet; Gaetan Bisson; Irene Bouw. Arithmetic, Geometry, Cryptography and Coding Theory: 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory, 770, ACM, 2021, Contemporary Mathematics, 978-1-4704-5426-5. ⟨10.48550/arXiv.2012.10805⟩. ⟨hal-03089551⟩
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