On the conjectures of Gross and Leopoldt

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Abstract

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
Volume22
Issue number5
DOIs
Publication statusPublished - 2015 Jan 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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