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.

引用

页码：361 / 371

页数：10

共 13 条

[1] Auel A., Brussel E., Garibaldi S., Vishne U., Open problems on central simple algebras, Transformation Groups, 16, pp. 219-264, (2011)
[2] Brussel E., McKinnie K., Tengan E., Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves, Advances in Mathematicas, 226, pp. 4316-4337, (2011)
[3] Brussel E., Tengan E., Formal constructions in the Brauer group of the function field of a p-adic curve, Transactions of the American Mathematical Society
[4] Brussel E., On Saltman’s p-adic curves papers, Quadratic Forms, Linear Algebraic Groups, and Cohomology, pp. 13-39, (2010)
[5] Garibaldi S., Merkurjev A., Serre J.-P., Cohomological Invariants in Galois Cohomology, (2003)
[6] Liu Q., Algebraic Geometry and Arithmetic Curves, (2002)
[7] Merkurjev A.S., Brauer groups of fields, Communications in Algebra, 11, pp. 2611-2624, (1983)
[8] Merkurjev A.S., Suslin A.A., K-cohomology of Seven Brauer varieties and the norm residue homomorphism, Mathematics of the USSR-Izvestiya, 21, pp. 307-340, (1983)
[9] Saltman D.J., Division algebras over p-adic curves, Journal of the Ramanujan Mathematical Society, 12, pp. 25-47, (1997)
[10] Saltman D.J., Correction to division algebras over p-adic curves, Journal of the Ramanujan Mathematical Society, 13, pp. 125-129, (1998)

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