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arXiv · 1003.1906

Tame division algebras of prime period over function fields of $p$-adic curves

E. Brussel·E. Tengan
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Abstract

Let F be a field of transcendence degree one over a p-adic field, and let l be a prime not equal to p. Results of Merkurjev and Saltman show that H^2(F,μ_l) is generated by Z/l-cyclic classes. We prove the "Z/l-length" in H^2(F,μ_l) equals the l-Brauer dimension, which Saltman showed to be two. It follows that all F-division algebras of period l are crossed products, either cyclic (by Saltman's cyclicity result) or tensor products of two cyclic division algebras. Our result was originally proved by Suresh assuming F contains μ_l.

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E. Brussel, E. Tengan. 2012-03-30. Tame division algebras of prime period over function fields of $p$-adic curves. https://arxiv.org/abs/1003.1906

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