Decomposition of Witt Rings and Galois Groups

Mináč, Ján ; Smith, Tara L.

Canadian journal of mathematics, Tome 47 (1995) no. 6, pp. 1274-1289

Résumé

To each field F of characteristic not 2, one can associate a certain Galois group GF , the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction of Witt rings corresponds to semidirect products of W-groups, and the basic part of W(F) is related to the center of GF . In an appendix we provide a complete list of Witt rings and corresponding w-groups for fields F with |Ḟ/Ḟ2| ≤ 16.

Détail

DOI : 10.4153/CJM-1995-065-0

Mots-clés : 11E81

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