Reciprocity maps with restricted ramification
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- by Romyar T. Sharifi PDF
- Trans. Amer. Math. Soc. 375 (2022), 5361-5392 Request permission
Abstract:
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.References
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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: sharifi@math.ucla.edu
- 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: https://doi.org/10.1090/tran/8658
- MathSciNet review: 4469223