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Projective Schur groups of iterated power series fields

โœ Scribed by Eli Aljadeff; Jack Sonn

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
130 KB
Volume
182
Category
Article
ISSN
0022-4049

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โœฆ Synopsis

The Brauer-Witt Theorem states that every Schur algebra over a รฟeld K is Brauer equivalent to a cyclotomic algebra. A central conjecture on the projective Schur group of a รฟeld is the analogue of this theorem, which asserts that every projective Schur algebra over a รฟeld K is Brauer equivalent to a radical algebra. The conjecture is so far known to be true in characteristic p and for local and global รฟelds. The next natural class of รฟelds to test is power series รฟelds over local and global รฟelds. In this paper we verify the conjecture for these รฟelds and more generally for iterated power series รฟelds over local and global รฟelds.

๐Ÿ“œ SIMILAR VOLUMES

On the Projective Schur Group of a Field
On the Projective Schur Group of a Field
โœ E. Aljadeff; J. Sonn ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 514 KB

If \(k\) is a field, the projective Schur group \(\operatorname{PS}(k)\) of \(k\) is the subgroup of the Brauer group \(\operatorname{Br}(k)\) consisting of those classes which contain a projective Schur algebra, i.e., a homomorphic image of a twisted group algebra \(k^{\text {" }} G\) with \(G\) fi