On 2-extensions of the rationals with restricted ramification

• Autorzy: Peter Schmid
• Języki publikacji: EN

Abstrakty

EN

For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).

Kategorie tematyczne

• 11F80: Galois representations
• 11R32: Galois theory
• 11S15: Ramification and extension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 2
• Strony: 111-125

Daty

wydano

2014

Twórcy

autor

Peter Schmid

• Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Identyfikatory

DOI

10.4064/aa163-2-2