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 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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On the conjectures of Gross and Leopoldt. / Seo, Soogil.
In: Mathematical Research Letters, Vol. 22, No. 5, 01.01.2015, p. 1509-1540.Research output: Contribution to journal › Article
TY - JOUR
T1 - On the conjectures of Gross and Leopoldt
AU - Seo, Soogil
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84964932867&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84964932867&partnerID=8YFLogxK
U2 - 10.4310/MRL.2015.v22.n5.a11
DO - 10.4310/MRL.2015.v22.n5.a11
M3 - Article
VL - 22
SP - 1509
EP - 1540
JO - Mathematical Research Letters
JF - Mathematical Research Letters
SN - 1073-2780
IS - 5
ER -