Realizing profinite reduced special groups

Vincent Astier and Hugo Mariano

Vol. 250 (2011), No. 2, 257–285

DOI: 10.2140/pjm.2011.250.257

Abstract

Special groups are an axiomatization of the algebraic theory of quadratic forms over fields. It is known that any finite reduced special group is the special group of some field. We show that any special group that is the projective limit of a projective system of finite reduced special groups is also the special group of some field.

Keywords

quadratic forms, special groups, projective limit, profinite, representation theorems

Mathematical Subject Classification 2000

Primary: 03C65, 11E81

Milestones

Received: 1 February 2010

Revised: 7 September 2010

Accepted: 19 October 2010

Published: 31 March 2011