Abstract

In this paper we solve some problems posed by Kolchin about differential algebraic groups. The main result (from which the others follow) is the embeddability of any differential algebraic group in an algebraic group. A crucial intermediate result, and one of independent interest, is a generalisation of Weil’s theorem on recovering an algebraic group from birational data, to pro-algebraic groups. 1. Introduction. Differential algebraic groups were introduced by Cassidy and Kolchin ([C1, 2] and [K2]), and have been studied by them and several others, notably Buium (e.g. [B1]). In fact interest in the subject has been given a boost by Buium’s recent work [B2] relating “finite- dimensional ” differential algebraic groups

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