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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:
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