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

被引：0
作者：
Brussel E. [1 ]
Tengan E. [2 ]
机构：
[1] Department of Mathematics, California Polytechnic State University, San Luis Obispo, 93407, CA
[2] Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo
来源：
Israel Journal of Mathematics | 2014年 / 201卷 / 1期
关键词：
Tensor Product; Group Theory; Function Field; Division Algebra; Transcendence Degree;
D O I：
10.1007/s11856-014-1082-3
中图分类号：
学科分类号：
摘要：
Let F be a field finitely generated and of transcendence degree one over a p-adic field, and let ℓ ≠ p be a prime. Results of Merkurjev and Saltman show that H2(F, µℓ) is generated by ℤ/ℓ-cyclic classes. We prove the “ℤ/ℓ-length” in H2(F, µℓ) is less than the ℓ-Brauer dimension, which Salt-man showed to be three. 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 F-division algebras. Our result was originally proved by Suresh when F contains the ℓ-th roots of unity µℓ. © 2014, Hebrew University of Jerusalem.
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页码：361 / 371
页数：10
相关论文
共 13 条
  • [11] Saltman D.J., Lectures on Division Algebras, (1999)
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  • [13] Suresh V., Bounding the symbol length in the Galois cohomology of function fields of p-adic curves, Commentarii Mathematici Helvetici, 85, pp. 337-346, (2010)
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