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Sato-Tate groups of genus 2 curves
Kiran S. Kedlaya
117 - 136
10.3233/978-1-61499-520-3-117
NATO Science for Peace and Security Series - D: Information and Communication Security
Volume 41: Advances on Superelliptic Curves and their Applications
Abstract

We describe the analogue of the Sato-Tate conjecture for an abelian variety over a number field; this predicts that the zeta functions of the reductions over various finite fields, when properly normalized, have a limiting distribution predicted by a certain group-theoretic construction related to Hodge theory, Galois images, and endomorphisms. After making precise the definition of the Sato-Tate group appearing in this conjecture, we describe the classification of Sato-Tate groups of abelian surfaces due to Fité–Kedlaya–Rotger–Sutherland.

$35.00 / €27.50 / £22.00
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