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 |
|---|---|
| Pages (from-to) | 1509-1540 |
| Number of pages | 32 |
| Journal | Mathematical Research Letters |
| Volume | 22 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2015 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Cite this
Seo, S. (2015). On the conjectures of Gross and Leopoldt. Mathematical Research Letters, 22(5), 1509-1540. https://doi.org/10.4310/MRL.2015.v22.n5.a11