Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields

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In this paper, we give a complete and explicit description of the splitting behavior of any place in a quintic trinomial dihedral or cyclic extension of a rational function field of finite characteristic distinct from 2 and 5. Our characterization depends only on the order of the base field and a parametrization of the coefficients of the generating trinomial. Moreover, we contrast some of our results to trinomial dihedral number fields of prime degree, where the unit rank behaves quite differently from the function field scenario
Publisher
SPRINGER
Issue Date
2012-01
Language
English
Article Type
Article
Keywords

IMAGINARY FUNCTION-FIELDS; RANK; SUBGROUPS

Citation

MANUSCRIPTA MATHEMATICA, v.137, no.1-2, pp.107 - 127

ISSN
0025-2611
DOI
10.1007/s00229-011-0459-4
URI
http://hdl.handle.net/10203/212938
Appears in Collection
MA-Journal Papers(저널논문)
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