Authors: Sergey V. Tikhonov, Jan Van Geel and Vyacheslav I. Yanchevskii: The unramified Brauer group and the Pythagoras number of hyperelliptic curves with good reduction defined over henselian valued fields.

jvg@cage.ugent.be, tsv@im.bas-net.by , yanch@im.bas-net.by

Submission: 2011, Jan 30

Let F be a henselian valued field with real closed residue field, C a hyperelliptic curve over F with good reduction. A set of independend generators for the two component of the Brauer group of C is calculated. As an application it is shown that the Pythagoras number of the function field F(C) of such curves is 2 if F(C) is a real field and 3 if F(C) is a non-real field.

2010 Mathematics Subject Classification:

Keywords and Phrases:

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