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Links between associated additive Galois modules and computation of H1 for local formal group modules. / Bondarko, M. V.

In: Journal of Number Theory, Vol. 101, No. 1, 01.07.2003, p. 74-104.

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

Harvard

Bondarko, MV 2003, 'Links between associated additive Galois modules and computation of H1 for local formal group modules', Journal of Number Theory, vol. 101, no. 1, pp. 74-104. https://doi.org/10.1016/S0022-314X(03)00019-2

APA

Bondarko, M. V. (2003). Links between associated additive Galois modules and computation of H1 for local formal group modules. Journal of Number Theory, 101(1), 74-104. https://doi.org/10.1016/S0022-314X(03)00019-2

Vancouver

Bondarko MV. Links between associated additive Galois modules and computation of H1 for local formal group modules. Journal of Number Theory. 2003 Jul 1;101(1):74-104. https://doi.org/10.1016/S0022-314X(03)00019-2

Author

Bondarko, M. V. / Links between associated additive Galois modules and computation of H1 for local formal group modules. In: Journal of Number Theory. 2003 ; Vol. 101, No. 1. pp. 74-104.

BibTeX

@article{0958497863d9447d9af96f6f3757f20f,
title = "Links between associated additive Galois modules and computation of H1 for local formal group modules",
abstract = "Using the methods described in the papers (Documenta Math. 5 (2000) 657; Local Leopoldt's problem for ideals in p-extensions of complete discrete valuation fields, to appear), we prove that a cocycle for a formal group in a Galois p-extension of a complete discrete valuation field is a coboundary if and only if the corresponding group algebra elements increase valuations by a number that is sufficiently large. We also calculate the valuation of the splitting element of a coboundary. A special case of the main theorem allows us to determine when a p-extension of a complete discrete valuation fields contains a root of a Kummer equation for a formal group. The theorem of Coates-Greenberg for formal group modules in deeply ramified extensions is generalized to noncommutative formal groups. Some results concerning finite torsion modules for formal groups are obtained.",
keywords = "Additive Galois module, Formal group, Group cohomology, Local field",
author = "Bondarko, {M. V.}",
year = "2003",
month = jul,
day = "1",
doi = "10.1016/S0022-314X(03)00019-2",
language = "English",
volume = "101",
pages = "74--104",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Links between associated additive Galois modules and computation of H1 for local formal group modules

AU - Bondarko, M. V.

PY - 2003/7/1

Y1 - 2003/7/1

N2 - Using the methods described in the papers (Documenta Math. 5 (2000) 657; Local Leopoldt's problem for ideals in p-extensions of complete discrete valuation fields, to appear), we prove that a cocycle for a formal group in a Galois p-extension of a complete discrete valuation field is a coboundary if and only if the corresponding group algebra elements increase valuations by a number that is sufficiently large. We also calculate the valuation of the splitting element of a coboundary. A special case of the main theorem allows us to determine when a p-extension of a complete discrete valuation fields contains a root of a Kummer equation for a formal group. The theorem of Coates-Greenberg for formal group modules in deeply ramified extensions is generalized to noncommutative formal groups. Some results concerning finite torsion modules for formal groups are obtained.

AB - Using the methods described in the papers (Documenta Math. 5 (2000) 657; Local Leopoldt's problem for ideals in p-extensions of complete discrete valuation fields, to appear), we prove that a cocycle for a formal group in a Galois p-extension of a complete discrete valuation field is a coboundary if and only if the corresponding group algebra elements increase valuations by a number that is sufficiently large. We also calculate the valuation of the splitting element of a coboundary. A special case of the main theorem allows us to determine when a p-extension of a complete discrete valuation fields contains a root of a Kummer equation for a formal group. The theorem of Coates-Greenberg for formal group modules in deeply ramified extensions is generalized to noncommutative formal groups. Some results concerning finite torsion modules for formal groups are obtained.

KW - Additive Galois module

KW - Formal group

KW - Group cohomology

KW - Local field

UR - http://www.scopus.com/inward/record.url?scp=0038008543&partnerID=8YFLogxK

U2 - 10.1016/S0022-314X(03)00019-2

DO - 10.1016/S0022-314X(03)00019-2

M3 - Article

AN - SCOPUS:0038008543

VL - 101

SP - 74

EP - 104

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -

ID: 49812779