On the conjectures of Gross and Leopoldt

Research output: Contribution to journalArticle

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

Fingerprint

Gross
Hilbert
Module
Cyclotomic
Theorem
Imply
Unit

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{d268da4e2ae647eab6c3db80e142d4c8,
title = "On the conjectures of Gross and Leopoldt",
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.",
author = "Soogil Seo",
year = "2015",
month = "1",
day = "1",
doi = "10.4310/MRL.2015.v22.n5.a11",
language = "English",
volume = "22",
pages = "1509--1540",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "5",

}

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 journalArticle

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 -