A generalized Iwasawa’s theorem and its application

Abstract

We generalize a theorem of Iwasawa on capitulation kernels of class groups over \({{\mathbb {Z}}}_p\)-extensions of number fields to all \({{\mathbb {Z}}}_p^d\)-extensions and discuss some of its applications.

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Correspondence to Ki-Seng Tan.

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K.-S. Tan: The author was supported in part by the Ministry of Science and Technology of Taiwan, MOST 103-2115-M-002-008-MY2, MOST 105-2115-M-002-009-MY2. It is our pleasure to thank NCTS/TPE for supporting a number of meetings of the authors in National Taiwan University

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Lai, K.F., Tan, KS. A generalized Iwasawa’s theorem and its application. Res Math Sci 8, 20 (2021). https://doi.org/10.1007/s40687-021-00258-3

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Keywords

  • \({\mathbb {Z}}_p^d\) extensions of number fields
  • Class groups
  • Capitulation map
  • Iwasawa theory

Mathematics Subject Classification

  • 11R29 (primary)
  • 11R23
  • 12G05
  • 11R65 (secondary)