Formal groups over discrete rings

Formal Groups over Discrete Rings

In this note we develop a theory of formal schemes and groups over arbitrary commutative rings which coincides with that of [5] if the base ring is a field, and generalizes that of [2]. We assume always our base ring is discrete and treat a formal scheme (resp. group) G, with two principal tools: A topology on the affine algebra (9(G) allows us to form its continuous linear dual B(G), the coalg...

Chevalley Groups over Commutative Rings

Orthogonal Groups over Local Rings

In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...

Endomorphism rings of almost full formal groups

Let oK be the integral closure of Zp in a finite field extension K of Qp, and let F be a one-dimensional full formal group defined over oK . We study certain finite subgroups C of F and prove a conjecture of Jonathan Lubin concerning the absolute endomorphism ring of the quotient F/C when F has height 2. We also investigate ways in which this result can be generalized to p-adic formal groups of...

Formal groups over Hopf algebras

The aim of this section is to define some generalization of the notion of formal group. More precisely, we consider the analog of formal groups with coefficients belonging to a Hopf algebra. We also study some example of a formal group over a Hopf algebra, which generalizes the formal group of geometric cobordisms. Recently some important connections between the Landweber-Novikov algebra and th...