Mathematics – Number Theory
Scientific paper
2005-03-28
Mat.Sb.,195 (2004), no. 6, 21-56
Mathematics
Number Theory
32 pages
Scientific paper
In this paper we study some special classes of division algebras over a Laurent series field with arbitrary residue field. We call the algebras from these classes as splittable and good splittable division algebras. It is shown that these classes contain the group of tame division algebras. For the class of good division algebras a decomposition theorem is given. This theorem is a generalization of the decomposition theorems for tame division algebras given by Jacob and Wadsworth. For both clases we introduce a notion of a $\delta$-map and develop a technique of $\delta$-maps for division algebras from these classes. Using this technique we reprove several old well known results of Saltman and get the positive answer on the period-index conjecture of M.Artin: the exponent of $A$ is equal to its index for any division algebra $A$ over a $C_2$-field $F$, when $F\eq F_1((t_2))$, where $F_1$ is a $C_1$-field. The paper includes also some other results about splittable division algebras, which, we hope, will be useful for the further investigation of wild division algebras.
No associations
LandOfFree
Wild division algebras over Laurent series fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Wild division algebras over Laurent series fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Wild division algebras over Laurent series fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-599225