Arithmetic invariants from Sato--Tate moments
Edgar Costa, Francesc Fit\'e, and Andrew V. Sutherland
TL;DR
This paper explores the arithmetic and geometric significance of Sato-Tate moments for abelian varieties, linking them to algebraic invariants like endomorphism ranks and Néron-Severi groups.
Contribution
It provides new interpretations of Sato-Tate moments in terms of the ranks of endomorphism and Néron-Severi groups of abelian varieties.
Findings
Relates Sato-Tate moments to endomorphism ring ranks.
Connects moments to Néron-Severi group ranks.
Offers geometric interpretations of arithmetic invariants.
Abstract
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 N\'eron-Severi group of A.
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