# Sato–Tate distributions and Galois endomorphism modules in genus 2

@article{Fite2012SatoTateDA,
title={Sato–Tate distributions and Galois endomorphism modules in genus 2},
author={Francesc Fit'e and Kiran S. Kedlaya and V{\'i}ctor Rotger and Andrew V. Sutherland},
journal={Compositio Mathematica},
year={2012},
volume={148},
pages={1390 - 1442}
}
• Published 30 October 2011
• Mathematics
• Compositio Mathematica
Abstract For an abelian surface A over a number field k, we study the limiting distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspond to taking characteristic polynomials 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…
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