The image of the natural homomorphism of Witt rings of orders in a global field
Volume 160 / 2013
Acta Arithmetica 160 (2013), 349-384
MSC: Primary 11E81; Secondary 19G12.
DOI: 10.4064/aa160-4-4
Abstract
Let $R$ be a Dedekind domain whose field of fractions is a global field. Moreover, let $\mathcal O < R$ be an order. We examine the image of the natural homomorphism $\varphi \colon W\mathcal {O}\to WR$ of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of $\varphi $ in the case of all nonreal quadratic number fields, all real quadratic number fields $K$ such that $-1$ is a norm in the extension $K/\mathbb Q$, and all quadratic function fields.
