Arithmetic invariants from Sato–Tate moments

Edgar Costa; Francesc Fité; Andrew V. Sutherland

doi:10.1016/j.crma.2019.11.008

Number theory

Arithmetic invariants from Sato–Tate moments
[Invariants arithmétiques provenant des moments de Sato–Tate]

Présenté par : the Editorial Board

Edgar Costa ¹ ; Francesc Fité ¹ ; Andrew V. Sutherland ¹

¹ Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, United States

Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 823-826.

Résumé
Abstract

Nous donons des interprétations arithmético-géométriques des moments $M_{2} [a_{1}]$ , $M_{1} [a_{2}]$ , et $M_{1} [s_{2}]$ du groupe de Sato–Tate d'une variété abélienne A definie sur un corps de nombres en les rapportant aux rangs de l'anneau d'endomorphismes et du groupe de Néron–Severi de A.

We give some arithmetic-geometric interpretations of the moments $M_{2} [a_{1}]$ , $M_{1} [a_{2}]$ , and $M_{1} [s_{2}]$ of the Sato–Tate group of an abelian variety A defined over a number field by relating them to the ranks of the endomorphism ring and Néron–Severi group of A.

Reçu le : 2019-10-08
Accepté le : 2019-11-19
Publié le : 2019-11-01

DOI : 10.1016/j.crma.2019.11.008

Affiliations des auteurs :

Edgar Costa ¹ ; Francesc Fité ¹ ; Andrew V. Sutherland ¹

¹ Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, United States

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     title = {Arithmetic invariants from {Sato{\textendash}Tate} moments},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {823--826},
     publisher = {Elsevier},
     volume = {357},
     number = {11-12},
     year = {2019},
     doi = {10.1016/j.crma.2019.11.008},
     language = {en},
}

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Edgar Costa; Francesc Fité; Andrew V. Sutherland. Arithmetic invariants from Sato–Tate moments. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 823-826. doi : 10.1016/j.crma.2019.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.11.008/

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