Sergey V. Tikhonov, Jan Van Geel, Vyacheslaw I. Yanchevskii: Pythagoras numbers of function fields of hyperelliptic curves with good reduction,,

Submission: 2004, Oct 5

It is shown that the Pythagoras number of a real function field of a hyperelliptic curve C with good reduction defined over the real formal power series field is equal to 2. A main tool in the proof is the explicit description of the Brauer group of C. If the function field of such a curve is non-real then it is shown that its Pythagoras number is 3.

2000 Mathematics Subject Classification: 11E10, 12D15, 12E15

Keywords and Phrases: Pythagoras number, Henselian discrete valued fields, Pythagorean fields, Brauer groups

Full text: dvi.gz 35 k, dvi 86 k, ps.gz 795 k, pdf.gz 208 k, pdf 233 k.

Server Home Page