On some sheaves of special groups

Using sheaves of special groups, we show that a general local-global principle holds for every reduced special group whose associated space of orderings only has a finite number of accumulation points. We also compute the behaviour of the Boolean hull functor applied to sheaves of special groups. The research leading to this note was carried out with the partial support of the European RTN Networks HPRN-CT-2002-00287 “Algebraic K-Theory, Linear Algebraic Groups and Related Structures”, and HPRN-CT-2001-00271 “Real Algebraic and Analytic Geometry”