Noncyclic division algebras over fields of Brauer dimension one

被引：1

作者：

Brussel, Eric ^{[1
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93405 USA

来源：

ADVANCES IN MATHEMATICS | 2020年 / 366卷

关键词：

Brauer group; Noncyclic division algebras; Cyclic division algebras; Brauer dimension; Symbol length; Period-index; Higher dimensional local field; Absolutely stable field; PERIOD-INDEX PROBLEM; U-INVARIANT;

D O I：

10.1016/j.aim.2020.107058

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a complete discretely valued field of rank one, with residue field Q(p). It is well known that period equals index in Br(K). We prove that when p = 2 there exist noncyclic K-division algebras of every 2-power degree divisible by four. Otherwise, every K-division algebra is cyclic. This gives the first published example of a field whose Brauer dimension and cyclic length are not equal. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：10

共 30 条

[1] Non-cyclic algebras of degree and exponent four [J].

Albert, A. Adrian .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1933, 35 (1-4) :112-121

[2]

[Anonymous], [No title captured]

[3]

[Anonymous], [No title captured]

[4]

[Anonymous], 2013, Algebraic number theory

[5] Cohomological obstruction theory for Brauer classes and the period-index problem [J].

Antieau, Benjamin .

JOURNAL OF K-THEORY, 2011, 8 (03) :419-435

[6]

ARASON JK, 1989, T AM MATH SOC, V313, P843

[7] Open problems on central simple algebras [J].

Auel, Asher ;

Brussel, Eric ;

Garibaldi, Skip ;

Vishne, Uzi .

TRANSFORMATION GROUPS, 2011, 16 (01) :219-264

[8] NONCROSSED PRODUCTS AND NONABELIAN CROSSED-PRODUCTS OVER Q(T) AND Q((T)) [J].

BRUSSEL, E .

AMERICAN JOURNAL OF MATHEMATICS, 1995, 117 (02) :377-393

[9] CYCLIC LENGTH IN THE TAME BRAUER GROUP OF THE FUNCTION FIELD OF A p-ADIC CURVE [J].

Brussel, Eric ;

McKinnie, Kelly ;

Tengan, Eduardo .

AMERICAN JOURNAL OF MATHEMATICS, 2016, 138 (02) :251-286

[10] The division algebras and Brauer group of a strictly henselian field [J].

Brussel, ES .

JOURNAL OF ALGEBRA, 2001, 239 (01) :391-411

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