The transfer ideal of quadratic forms and a hasse norm theorem mod squares

David B. Leep, Adrian R. Wadsworth

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Any finite degree field extension K/F determines an ideal Ik/f of the Witt ring WF of F, called the transfer ideal, which is the image of any nonzero transfer map WK → WF. The ideal Ik/f is computed for certain field extensions, concentrating on the case where K has the form F(√ a1;,&, √ an), aiε F. When F and K are global fields, we investigate whether there is a local global principle for membership in Ik/f. This is shown to be equivalent to the existence of a "Hasse norm theorem mod squares, " i.e., a local global principle for the image of the norm map NK/F: KK2→ F/F2. It is shown that such a Hasse norm theorem holds whenever K = F(√ a1;,&, √ an), although it does not always hold for more general extensions of global fields, even some Galois extensions with group Z/2Z × Z/4Z.

Original languageEnglish
Pages (from-to)415-431
Number of pages17
JournalTransactions of the American Mathematical Society
Volume315
Issue number1
DOIs
StatePublished - Sep 1989

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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