David.Grimm@uni-konstanz.de

Submission: 2008, Oct 6

We show as the main result, that the Pythagoras number of the function field of a conic is 2, only if the ground field is hereditarily pythagorean. Furthermore, we consider function fields of certain quadrics and prove some 'Going Down'-results for the finiteness of the Pythagoras number from the function field to the ground field (and all its finite extensions).

2000 Mathematics Subject Classification: 11E10, 12D15, 14H05, 12F10, 12J10, 14H05

Keywords and Phrases: Pythagoras number, Quadrics, Conics, Hereditarily Pythagorean Fields

Full text: dvi.gz 30 k, dvi 82 k, ps.gz 631 k, pdf.gz 156 k, pdf 186 k.

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