Arithmetic invariants from Sato–Tate moments

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2019Embargo end date: 01 Jan 2019 English Publisher:Cellule MathDoc/Centre MersenneJournal:Comptes Rendus. Mathématique, volume 357, pages 823-826 (issn: 1631-073X, eissn: 1778-3569,

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

doi: 10.1016/j.crma.2019.11.008 , 10.48550/arxiv.1910.00518

arXiv: 1910.00518

handle: 2072/378025

Arithmetic invariants from Sato–Tate moments

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Abstract

We give some arithmetic-geometric interpretations of the moments M2[a1], M1[a2], and M1[s2] 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.

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Massachusetts Institute of Technology
United States

Keywords

11M50 (Primary) 11G10, 14K15 (Secondary), Mathematics - Number Theory, abelian variety, Néron-Severi group, Sato-Tate group, Abelian varieties of dimension \(> 1\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Relations with random matrices, Arithmetic ground fields for abelian varieties, FOS: Mathematics, Matemàtiques, Number Theory (math.NT), 51 - Matemàtiques

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NOETHER–LEFSCHETZ THEORY AND NÉRON–SEVERI GROUP
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