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Sato-Tate distributions and Galois endomorphism modules in genus 2

Autor
Fite, F.; Kedlaya, K.; Rotger, V.; Sutherland, A.
Tipus d'activitat
Article en revista
Revista
Compositio mathematica
Data de publicació
2012
Volum
148
Número
5
Pàgina inicial
1390
Pàgina final
1442
DOI
https://doi.org/10.1112/S0010437X12000279 Obrir en finestra nova
Projecte finançador
Aritmética de variedades algebraicas: teoría y computación
Repositori
http://hdl.handle.net/2117/18029 Obrir en finestra nova
Resum
For an abelian surface A over a number eld k, we study the limit- ing distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to taking characteristic poly- nomials of a uniform random matrix in some closed subgroup of USp(4); this Sato-Tate group may be obtained from the Galois action on any Tate module of A. We show that the Sato-Tate group is limited to a particular list of 55 groups up to conjugacy. We then classify A according to the...
Citació
Fité, F. [et al.]. Sato-Tate distributions and Galois endomorphism modules in genus 2. "Compositio mathematica", 2012, vol. 148, núm. 5, p. 1390-1442.
Paraules clau
Galois type, Sato-Tate distributions, abelian surfaces, endomorphism algebras
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

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