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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Rigorous computation of the endomorphism ring of a Jacobian
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by Edgar Costa, Nicolas Mascot, Jeroen Sijsling and John Voight HTML | PDF
Math. Comp. 88 (2019), 1303-1339 Request permission

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
  • MR Author ID: 1041071
  • ORCID: 0000-0003-1367-7785
  • 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
  • MR Author ID: 1040021
  • Email: nm116@aub.edu.lb
  • Jeroen Sijsling
  • Affiliation: Universität Ulm, Institut für Reine Mathematik, D-89068 Ulm, Germany
  • MR Author ID: 974789
  • ORCID: 0000-0002-0632-9910
  • Email: jeroen.sijsling@uni-ulm.de
  • John Voight
  • Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
  • MR Author ID: 727424
  • ORCID: 0000-0001-7494-8732
  • Email: jvoight@gmail.com
  • 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).
  • © Copyright 2018 American Mathematical Society
  • Journal: Math. Comp. 88 (2019), 1303-1339
  • MSC (2010): Primary 11G10, 11Y99, 14H40, 14K15, 14Q05
  • DOI: https://doi.org/10.1090/mcom/3373
  • MathSciNet review: 3904148