TY - JOUR
T1 - Local-global principles for witt rings
AU - Efrat, Ido
N1 - Funding Information:
Correspondence to: 1. Efrat, Fakult?it fiir Mathematik, Konstanz, Germany. * The work was partially supported by grants from Lion’s foundation Foundation for Scientific Research and Development.
PY - 1993/12/1
Y1 - 1993/12/1
N2 - This paper investigates the connection between the Witt and Witt-Grothendieck rings of a field K and the corresponding rings of a given collection K of separable algebraic extensions of K. In particular, it deals with the question whether the former rings are the "sheaf products" of the latter rings. If K consists of pro-2 extensions and is closed in the natural topology then this happens precisely when the 2-Galois group of K is the free pro-2 product of the 2-Galois groups of the fields in K. This result is used to classify the quadratic forms over the field of totally real numbers, and more generally, over real-projective fields.
AB - This paper investigates the connection between the Witt and Witt-Grothendieck rings of a field K and the corresponding rings of a given collection K of separable algebraic extensions of K. In particular, it deals with the question whether the former rings are the "sheaf products" of the latter rings. If K consists of pro-2 extensions and is closed in the natural topology then this happens precisely when the 2-Galois group of K is the free pro-2 product of the 2-Galois groups of the fields in K. This result is used to classify the quadratic forms over the field of totally real numbers, and more generally, over real-projective fields.
UR - http://www.scopus.com/inward/record.url?scp=38248998663&partnerID=8YFLogxK
U2 - 10.1016/0022-4049(93)90127-F
DO - 10.1016/0022-4049(93)90127-F
M3 - Article
AN - SCOPUS:38248998663
SN - 0022-4049
VL - 90
SP - 153
EP - 166
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 2
ER -