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arXiv · 1408.6968

Sato-Tate groups of genus 2 curves

Kiran S. Kedlaya
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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 Fite-Kedlaya-Rotger-Sutherland. (These are notes from a three-lecture series presented at the NATO Advanced Study Institute "Arithmetic of Hyperelliptic Curves" held in Ohrid (Macedonia) August 25-September 5, 2014, and are expected to appear in a proceedings volume.)

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Kiran S. Kedlaya. 2014-12-11. Sato-Tate groups of genus 2 curves. https://arxiv.org/abs/1408.6968

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