# 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} }

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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