This article is cited in 1 paper

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.

UDC: 512.741.5

Received: 04.02.2004
Revised: 04.12.2006

DOI: 10.4213/mzm3801

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

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