On number fields with power-free discriminant

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Given a finite transitive permutation group G, we investigate number fields F/DOUBLE-STRUCK CAPITAL Q of Galois group G whose discriminant is only divisible by small prime powers. This generalizes previous investigations of number fields with squarefree discriminant. In particular, we obtain a comprehensive result on number fields with cubefree discriminant. Our main tools are arithmetic-geometric, involving in particular an effective criterion on ramification in specializations of Galois covers.
Publisher
HEBREW UNIV MAGNES PRESS
Issue Date
2020-01
Language
English
Article Type
Article
Citation

ISRAEL JOURNAL OF MATHEMATICS, v.235, no.1, pp.413 - 437

ISSN
0021-2172
DOI
10.1007/s11856-020-1962-7
URI
http://hdl.handle.net/10203/282124
Appears in Collection
RIMS Journal Papers
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