Arithmetic invariants from Sato–Tate moments

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

doi:10.1016/j.crma.2019.11.008

Number theory

Arithmetic invariants from Sato–Tate moments

Presented by: the Editorial Board

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

Abstract
Résumé

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.

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.

Received: 2019-10-08
Accepted: 2019-11-19
Published online: 2019-11-01

DOI: 10.1016/j.crma.2019.11.008

Author's affiliations:

Costa, Edgar ¹; Fité, Francesc ¹; Sutherland, Andrew V. 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},
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Costa, Edgar; Fité, Francesc; Sutherland, Andrew V. 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. http://archive.numdam.org/articles/10.1016/j.crma.2019.11.008/

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