Tame division algebras of prime period over function fields of p-adic curves |
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Authors: | Eric Brussel Eduardo Tengan |
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Institution: | 1. Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA, 93407, USA 2. Instituto de Ciências Matemáticas e de Computa??o, Universidade de S?o Paulo, S?o Carlos, S?o Paulo, Brazil
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Abstract: | Let F be a field finitely generated and of transcendence degree one over a p-adic field, and let ? ≠ p be a prime. Results of Merkurjev and Saltman show that H2(F, µ?) is generated by ?/?-cyclic classes. We prove the “?/?-length” in H2(F, µ?) is less than the ?-Brauer dimension, which Salt-man showed to be three. It follows that all F-division algebras of period ? are crossed products, either cyclic (by Saltman’s cyclicity result) or tensor products of two cyclic F-division algebras. Our result was originally proved by Suresh when F contains the ?-th roots of unity µ?. |
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