Some foundational questions concerning differential algebraic groups

Anand Pillay

Vol. 179 (1997), No. 1, 179–200

DOI: 10.2140/pjm.1997.179.179

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.

Milestones

Received: 28 July 1993

Revised: 11 September 1996

Published: 1 May 1997