Harrison's criterion
characterizes the isomorphy of the Witt rings of two fields in terms
of properties of these fields. In this article, we discuss about the
existence of such characterizations for the isomorphism of Witt
groups of hermitian forms over certain algebras with involution. In
the cases where we consider the Witt group of a quadratic extension
with its non-trivial automorphism or the Witt group of a quaternion
division algebra with its canonical involution, such criteria are
proved. In the framework of global fields, these
criteria are reformulated in terms of properties involving
certain real places of the considered fields.
Publié le : 2009-08-15
Classification:
Harrison's criterion,
Witt equivalence,
reciprocity equivalence,
algebras with involution,
11E39,
11E81
@article{1251832376,
author = {Grenier-Boley, N.},
title = {Harrison's criterion, Witt equivalence and reciprocity equivalence},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {16},
number = {1},
year = {2009},
pages = { 509-523},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832376}
}
Grenier-Boley, N. Harrison's criterion, Witt equivalence and reciprocity equivalence. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp. 509-523. http://gdmltest.u-ga.fr/item/1251832376/