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

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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)

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10.4310/MRL.2015.v22.n5.a11

Cite this

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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).",

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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.

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On the conjectures of Gross and Leopoldt

Abstract

Bibliographical note

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