Arithmetic invariants from Sato-Tate moments. (Invariants arithmétiques provenant des moments de Sato-Tate.) (English. French summary) Zbl 1444.11127

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

C. R., Math., Acad. Sci. Paris 357, No. 11-12, 823-826 (2019).

Summary: We give some arithmetic-geometric interpretations of the moments \(\operatorname{M}_2 [a_1]\), \(\operatorname{M}_1 [a_2]\), and \(\operatorname{M}_1 [s_2]\) 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 \(A\).

MSC:

11G10	Abelian varieties of dimension \(> 1\)
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14K15	Arithmetic ground fields for abelian varieties
11M50	Relations with random matrices

Keywords:

Sato-Tate group; abelian variety; Néron-Severi group

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