On absolute Galois splitting fields of central simple algebras
نویسندگان
چکیده
منابع مشابه
On Absolute Galois Splitting Fields of Central Simple Algebras
A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper proves an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and all twisted Laurent series rings over symbol algebras (or p-algebras) over global fields are cross...
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Let A1, . . . , An be central simple algebras over a field F . Suppose that we possess an information on the Schur indexes of some tensor products of (some tensor powers of) the algebras. What can be said (in general) about possible degrees of finite field extensions of F splitting the algebras? In Part I, we prove a positive result of that kind. In Part II, we prove a negative result. In Part ...
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We provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra. c © 2006 Elsevier Ltd. All rights reserved.
متن کاملOn the Descending Central Sequence of Absolute Galois Groups
Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F . Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p , or the modular group Mp3 of order p .
متن کاملOn the Descending Central Sequence of Absolute Galois Groups
Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F . Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p , or the extra-special group Mp3 of order p and exponent p.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.12.011