Division Algebras over Henselian Fields
Bill Jacob,Adrian R. Wadsworth +1 more
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TL;DR: In this paper, the authors focus on the tame division algebras D with center a field F with Henselian valuation v. As usual, they approach this by first obtaining results for graded division algebra, then lifting back from \(\operatorname {\mathsf {gr}}(D)\) to D. This is facilitated by results in §8.4.
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About: This article is published in Journal of Algebra. The article was published on 01 Jan 1990. and is currently open access. The article focuses on the topics: Center (category theory) & Division algebra.
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Citations
Graded Hermitian forms and Springer's theorem
TL;DR: In this paper, an analogue of Springer's theorem on the Witt group of quadratic forms over a complete discretely valued field is proved for Hermitian forms over division algebras over a Henselian field, including some cases where the residue characteristic is 2.
25
SK1 of graded division algebras
TL;DR: In this article, the reduced Whitehead group SK1 of a graded division algebra graded by a torsion-free abelian group is studied, and it is observed that the computations here are much more straightforward than in the non-graded setting.
•Posted Content
Cyclic Algebras over $p$-adic curves
TL;DR: In this article, it was shown that cyclic division algebras of degree (and hence exponent) are cyclic and a geometric criterion for a Brauer class to have index ≥ 0.
23
SK1-like Functors for Division Algebras
TL;DR: In this paper, the authors investigated the group valued functor G (D ) for the reduced Whitehead group SK 1 and established a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra.
21
The “Defektsatz” for central simple algebras
TL;DR: In this article, the intersection property of Dubrovin valuation rings is defined in terms of the prime ideals and the valuation overrings of the intersection B ∩...∩B n.
References
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Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
- 01 Jan 1977
8.5K
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Algebraic Number Theory
Serge Lang
- 01 Jan 1971
TL;DR: The second edition of Lang's well-known textbook as mentioned in this paper contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties.
2.6K
On central division algebras
TL;DR: For any integern such that 8|n or for which there exists an odd primeq such thatq 2|n, there is a central division algebra of dimensionn 2 over its center which is not a crossed product as mentioned in this paper.
140
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