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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Reciprocity maps with restricted ramification
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by Romyar T. Sharifi PDF
Trans. Amer. Math. Soc. 375 (2022), 5361-5392 Request permission


We compare two maps that arise in study of the cohomology of global fields with ramification restricted to a finite set $S$ of primes. One of these maps, which we call an $S$-reciprocity map, interpolates the values of cup products in $S$-ramified cohomology. In the case of $p$-ramified cohomology of the $p$th cyclotomic field for an odd prime $p$, we use this to exhibit an intriguing relationship between particular values of the cup product on cyclotomic $p$-units. We then consider higher analogues of the $S$-reciprocity map and relate their cokernels to the graded quotients in augmentation filtrations of Iwasawa modules.
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Additional Information
  • Romyar T. Sharifi
  • Affiliation: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
  • MR Author ID: 621651
  • ORCID: 0000-0003-0675-1692
  • Email:
  • Received by editor(s): November 1, 2020
  • Received by editor(s) in revised form: July 17, 2021
  • Published electronically: June 10, 2022
  • Additional Notes: The author’s research was supported in part the National Science Foundation under Grant No. DMS-1801963. Part of the research for this article took place during stays at the Max Planck Institute for Mathematics, the Institut des Hautes Études Scientifiques, and the Fields Institute.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 5361-5392
  • MSC (2020): Primary 11R34; Secondary 11R23, 11R27, 11R29
  • DOI:
  • MathSciNet review: 4469223