{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T05:19:13Z","timestamp":1740028753875,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>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 Fit&amp;eacute;&amp;ndash;Kedlaya&amp;ndash;Rotger&amp;ndash;Sutherland.<\/jats:p>","DOI":"10.3233\/978-1-61499-520-3-117","type":"book-chapter","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:11:46Z","timestamp":1739992306000},"source":"Crossref","is-referenced-by-count":0,"title":["Sato-Tate groups of genus 2 curves"],"prefix":"10.3233","author":[{"family":"Kedlaya Kiran S.","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["NATO Science for Peace and Security Series - D: Information and Communication Security","Advances on Superelliptic Curves and their Applications"],"original-title":[],"deposited":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:18:27Z","timestamp":1739992707000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISBN&isbn=978-1-61499-519-7&spage=117&doi=10.3233\/978-1-61499-520-3-117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-61499-520-3-117","relation":{},"ISSN":["1874-6268"],"issn-type":[{"value":"1874-6268","type":"print"}],"subject":[],"published":{"date-parts":[[2015]]}}}