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Mathematics of Computation

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Rigorous computation of the endomorphism ring of a Jacobian


Authors: Edgar Costa, Nicolas Mascot, Jeroen Sijsling and John Voight
Journal: Math. Comp. 88 (2019), 1303-1339
MSC (2010): Primary 11G10, 11Y99, 14H40, 14K15, 14Q05
DOI: https://doi.org/10.1090/mcom/3373
Published electronically: September 10, 2018
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Abstract: We describe several improvements and generalizations to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.


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Additional Information

Edgar Costa
Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
Address at time of publication: Department of Mathematics, 77 Massachusetts Ave., Bldg. 2-252B, Cambridge, Massachusetts 02139
Email: edgarc@mit.edu

Nicolas Mascot
Affiliation: Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
Address at time of publication: Department of Mathematics, Faculty of Arts and Sciences, American University of Beirut, P.O. Box 11-0236, Riad El Solh, Beirut 1107 2020, Lebanon
Email: nm116@aub.edu.lb

Jeroen Sijsling
Affiliation: Universität Ulm, Institut für Reine Mathematik, D-89068 Ulm, Germany
Email: jeroen.sijsling@uni-ulm.de

John Voight
Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
Email: jvoight@gmail.com

DOI: https://doi.org/10.1090/mcom/3373
Received by editor(s): May 30, 2017
Received by editor(s) in revised form: January 14, 2018, and April 4, 2018
Published electronically: September 10, 2018
Additional Notes: The second author was supported by the EPSRC Programme Grant EP/K034383/1 “LMF: L-Functions and Modular Forms”.
The third author was supported by the Juniorprofessuren-Programm “Endomorphismen algebraischer Kurven” (7635.521(16)) from the Science Ministry of Baden–Württemberg.
The fourth author was supported by an NSF CAREER Award (DMS-1151047) and a Simons Collaboration Grant (550029).
Article copyright: © Copyright 2018 American Mathematical Society