On the conjectures of Gross and Leopoldt

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We show that the Leopoldt conjecture implies the so-called Hilbert's theorem 90 for compact modules made from the p-units over the cyclotomic ℤp-extension κcyc∞ of κ. And under the generalized Gross conjecture, we show that Hilbert fs theorem 90 for the compact modules above is equivalent to the affirmation of the Leopoldt conjecture.

Original languageEnglish
Pages (from-to)1509-1540
Number of pages32
JournalMathematical Research Letters
Issue number5
Publication statusPublished - 2015

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP)(No. 2014001824).

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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