Period-index and u-invariant questions for function fields over complete discretely valued fields

Abstract

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 give a bound for the Brauer p-simension of F in terms of 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.

References in corpus (3)

• Applications of patching to quadratic forms and central simple algebras
• Quadric surface bundles over surfaces
• Colliot-Thélène's conjecture and finiteness of u-invariants

Cited by in corpus (14)

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• On the Brauer $p$-dimension of Henselian discrete valued fields of residual characteristic $p>0$
• Trivialité des groupes de Whitehead réduits avec applications à l'approximation faible et l'approximation forte
• Period-index bounds for arithmetic threefolds
• Linkage of Pfister forms over semi-global fields
• Lower bounds and infinity criterion for Brauer $p$-dimensions of finitely-generated field extensions
• Cyclicity and indecomposability in the Brauer group of a $p$-adic curve