Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE LOWER LAYERS OF A ℤp-EXTENSION

  • Oh, Jangheon (Department of Mathematics and Statistics, Sejong University)
  • Received : 2021.12.18
  • Accepted : 2022.06.09
  • Published : 2022.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

It is shown that the p-part of the class number of the lower layers of a cyclotomic ℤp-extension can grow exponentially.

Keywords

References

  1. K.Iwasawa, On ℤ𝓁-extensions of algebraic number fields, Ann.of Math. 98 (2) (1973), 246-326. https://doi.org/10.2307/1970784
  2. T.Kataoka, A consequence of Greenberg's generalized conjecture on Iwasawa invariants of ℤp-extensions, Journal of Number Theory 172 (3) (2017), 200-233. https://doi.org/10.1016/j.jnt.2016.08.008
  3. J.Minardi, Iwasawa modules for ℤdp-extensions of algebraic number fields, Ph.D dissertation, University of Washington, 1986.
  4. L.Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math., 83, Springer-Verlag, New York(1982).