Number theory
Arithmetic invariants from Sato–Tate moments
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 823-826.

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.

Nous donons des interprétations arithmético-géométriques des moments M2[a1], M1[a2], et M1[s2] 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.

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Published online:
DOI: 10.1016/j.crma.2019.11.008
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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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://www.numdam.org/articles/10.1016/j.crma.2019.11.008/

[1] Banaszak, G.; Kedlaya, K.S. An algebraic Sato–Tate group and Sato–Tate conjecture, Indiana Univ. Math. J., Volume 64 (2015), pp. 245-274

[2] Cantoral Farfán, V.; Commelin, J. The Mumford–Tate conjecture implies the algebraic Sato–Tate conjecture of Banaszak and Kedlaya | arXiv

[3] Faltings, G. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., Volume 73 (1983), pp. 349-366

[4] Fité, F.; Kedlaya, K.S.; Sutherland, A.V.; Rotger, V. Sato–Tate distributions and Galois endomorphism modules in genus 2, Compos. Math., Volume 148 (2012), pp. 1390-1442

[5] Kim, S. The Sato–Tate conjecture and Nagao's conjecture | arXiv

[6] Mumford, D. Abelian Varieties, Tata Institute of Fundamental Research, Bombay, Oxford University Press, 1970

[7] Serre, J.-P. Linear Representations of Finite Groups, Springer-Verlag, New York, 1977

[8] Serre, J.-P. Lectures on NX(p), CRC Press, Boca Raton, FL, USA, 2012

[9] Tate, J. Algebraic cycles and poles of zeta functions, 5–7 December 1963, Harper & Row, New York (1965), pp. 93-110

[10] Tate, J. Endomorphisms of abelian varieties over finite fields, Invent. Math., Volume 2 (1966), pp. 134-144

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