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

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

2010-03-09

arxiv.org/abs/1003.1906v3

Mathematics

Number Theory

We correct some minor inaccuracies in the introduction

Scientific paper

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,\mu_l) is generated by Z/l-cyclic classes. We prove the "Z/l-length" in H^2(F,\mu_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 \mu_l.

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