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 language | English |
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Pages (from-to) | 1509-1540 |
Number of pages | 32 |
Journal | Mathematical Research Letters |
Volume | 22 |
Issue number | 5 |
DOIs | |
Publication status | Published - 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)