On the conjectures of Gross and Leopoldt

Soogil Seo

doi:10.4310/MRL.2015.v22.n5.a11

On the conjectures of Gross and Leopoldt

Soogil Seo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 ℤ_p-extension κ^cyc∞ 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	https://doi.org/10.4310/MRL.2015.v22.n5.a11
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)

Access to Document

10.4310/MRL.2015.v22.n5.a11

Fingerprint Dive into the research topics of 'On the conjectures of Gross and Leopoldt'. Together they form a unique fingerprint.

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",

note = "Funding Information: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP)(No. 2014001824).",

year = "2015",

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",

}

TY - JOUR

T1 - On the conjectures of Gross and Leopoldt

AU - Seo, Soogil

N1 - Funding Information: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP)(No. 2014001824).

PY - 2015

Y1 - 2015

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

AN - SCOPUS:84964932867

VL - 22

SP - 1509

EP - 1540

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 5

ER -

On the conjectures of Gross and Leopoldt

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this