Submission: 2013, Apr 8
Let K be a complete discretely valued field and F the function field of a curve over K. If the characteristic of the residue field k of K is p > 0, then we show that the Brauer p-simension of F is bounded by the p-rank of k. If k is a perfect field of characteristic 2, we show that the u-invaraint of F is at most 8.
2010 Mathematics Subject Classification:
Keywords and Phrases: Brauer dimension, u-invariant, function fields, complete discrete valued fields.
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