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 Mat. Zametki, 2007, Volume 82, Issue 2, Pages 183–189 (Mi mz3801)

Canonical Representatives in Strict Isomorphism Classes of Formal Groups

M. V. Bondarko

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: The aim of the present paper is to explicitly construct canonical representatives in every strict isomorphism class of commutative formal groups over an arbitrary torsion-free ring. The case of an $\mathbb Z_{(p)}$-algebra is treated separately. We prove that, under natural conditions on a subring, the canonical representatives of formal groups over the subring agree with the representatives for the ring. Necessary and sufficient conditions for a mapping induced on strict isomorphism classes of formal groups by a homomorphism of torsion-free rings to be injective and surjective are established.

Keywords: commutative formal group, strict isomorphism, torsion-free ring, canonical representatives, universal curvilinear law

DOI: https://doi.org/10.4213/mzm3801

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English version:
Mathematical Notes, 2007, 82:2, 159–164

Bibliographic databases:

UDC: 512.741.5
Revised: 04.12.2006

Citation: M. V. Bondarko, “Canonical Representatives in Strict Isomorphism Classes of Formal Groups”, Mat. Zametki, 82:2 (2007), 183–189; Math. Notes, 82:2 (2007), 159–164

Citation in format AMSBIB
\Bibitem{Bon07} \by M.~V.~Bondarko \paper Canonical Representatives in Strict Isomorphism Classes of Formal Groups \jour Mat. Zametki \yr 2007 \vol 82 \issue 2 \pages 183--189 \mathnet{http://mi.mathnet.ru/mz3801} \crossref{https://doi.org/10.4213/mzm3801} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2374896} \elib{http://elibrary.ru/item.asp?id=12844013} \transl \jour Math. Notes \yr 2007 \vol 82 \issue 2 \pages 159--164 \crossref{https://doi.org/10.1134/S0001434607070206} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000249410700020} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-58649123122} 

• http://mi.mathnet.ru/eng/mz3801
• https://doi.org/10.4213/mzm3801
• http://mi.mathnet.ru/eng/mz/v82/i2/p183

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This publication is cited in the following articles:
1. Vostokov S.V., Afanas'eva S.S., Bondarko M.V., Volkov V.V., Demchenko O.V., Ikonnikova E.V., Zhukov I.B., Nekrasov I.I., Pital P.N., “Explicit Constructions and the Arithmetic of Local Number Fields”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 242–264
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