The twisting Sato–Tate group of the curve y 2 = x 8 - 14 x 4 + 1

We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve y2=x8-14x4+1 and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of y2=x8-14x4+1. Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobia...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 290; no. 3; pp. 991 - 1022
Main Authors Arora, Sonny, Cantoral-Farfán, Victoria, Landesman, Aaron, Lombardo, Davide, Morrow, Jackson S
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2018
Subjects
Chemical industry
Jacobians
Subgroups
Twisting
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Summary:We determine the twisting Sato–Tate group of the genus 3 hyperelliptic curve y2=x8-14x4+1 and show that all possible subgroups of the twisting Sato–Tate group arise as the Sato–Tate group of an explicit twist of y2=x8-14x4+1. Furthermore, we prove the generalized Sato–Tate conjecture for the Jacobians of all Q-twists of the curve y2=x8-14x4+1.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-018-2049-6