USP Electronic Research Repository

Crossed product orders over valuation rings II: Tamely ramified crossed product algebras

Kauta, John S. and Marubayashi, H. and Miyamoto, H. (2003) Crossed product orders over valuation rings II: Tamely ramified crossed product algebras. Bulletin of the London Mathematical Society, 35 (4). pp. 541-552. ISSN 0024-6093

[img] PDF - Accepted Version
Restricted to Registered users only

Download (130Kb)

    Abstract

    Let V be a commutative valuation domain of arbitrary K rull-dimension, with quotient field F, let K be a finite Galois extension of F with group G, and let S be the integral closure of V in K. Suppose that one has a 2-cocycle on G that takes values in the group of units of S. Then one can form the crossed product of G over S, S * G, which is a V-order in the central simple F-algebra K * G. If S * G is assumed to be a Dubrovin valuation ring of K * G, then the main result of this paper is that, given a suitable definition of tameness for central simple algebras, K * G is tamely ramified and defectless over F if and only if K is tamely ramified and defectless over F. The residue structure of S * G is also considered in the paper, as well as its behaviour upon passage to Henselization.

    Item Type: Journal Article
    Subjects: Q Science > QA Mathematics
    Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
    Depositing User: John Kauta
    Date Deposited: 06 Nov 2013 11:45
    Last Modified: 06 Nov 2013 11:45
    URI: http://repository.usp.ac.fj/id/eprint/7011
    UNSPECIFIED

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...