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Transactions of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access electronic-only journal is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 2330-0000

The 2020 MCQ for Transactions of the American Mathematical Society Series B is 1.73.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On unit signatures and narrow class groups of odd degree abelian number fields
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by Benjamin Breen, Ila Varma and John Voight; with an appendix by Noam Elkies
Trans. Amer. Math. Soc. Ser. B 10 (2023), 86-128
DOI: https://doi.org/10.1090/btran/90
Published electronically: February 3, 2023

Abstract:

For an abelian number field of odd degree, we study the structure of its $2$-Selmer group as a bilinear space and as a Galois module. We prove structural results and make predictions for the distribution of unit signature ranks and narrow class groups in families where the degree and Galois group are fixed.
References
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Bibliographic Information
  • Benjamin Breen
  • Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
  • Email: benjamin.k.breen.gr@dartmouth.edu
  • Ila Varma
  • Affiliation: Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George Street, Toronto, Ontario M5S 2E4
  • MR Author ID: 960137
  • Email: ila@math.toronto.edu
  • John Voight
  • MR Author ID: 727424
  • ORCID: 0000-0001-7494-8732
  • Noam Elkies
  • Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
  • MR Author ID: 229330
  • Email: jvoight@gmail.com
  • Received by editor(s): June 7, 2021
  • Received by editor(s) in revised form: July 18, 2021
  • Published electronically: February 3, 2023
  • Additional Notes: Breen was partially supported by an NSF Grant (DMS-1547399). Varma was partially supported by an NSF MSPRF Grant (DMS-1502834) and an NSF Grant (DMS-1844206). Voight was supported by an NSF CAREER Award (DMS-1151047) and a Simons Collaboration Grant (550029). Elkies was partially supported by an NSF grant (DMS-1502161) and a Simons Collaboration Grant.
  • © Copyright 2023 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
  • Journal: Trans. Amer. Math. Soc. Ser. B 10 (2023), 86-128
  • MSC (2020): Primary 11R29, 11R27, 11R45, 11Y40
  • DOI: https://doi.org/10.1090/btran/90
  • MathSciNet review: 4544138