Geodesic
The image of the natural homomorphism of Witt rings of orders in a global field
Beata Rothkegel1
1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland
Acta Arithmetica, Tome 160 (2013) no. 4, pp. 349-384.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa160-4-4
Keywords: dedekind domain whose field fractions global field moreover mathcal order examine image natural homomorphism varphi colon mathcal corresponding witt rings formulate necessary sufficient conditions surjectivity varphi nonreal quadratic number fields real quadratic number fields norm extension mathbb quadratic function fields

Beata Rothkegel 1

1 Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland 
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Beata Rothkegel. The image of the natural homomorphism of Witt rings of orders in a global field. Acta Arithmetica, Tome 160 (2013) no. 4, pp. 349-384. doi : 10.4064/aa160-4-4. http://geodesic.mathdoc.fr/articles/10.4064/aa160-4-4/

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