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On representations of the Weil group with bounded conductor. (English) Zbl 0849.11086

Summary: It is shown that there are only finitely many representations of the Weil group of \(\mathbb{Q}\) having given dimension, conductor, and infinity type. In particular, the number of Galois representations of given dimension and conductor is finite. The proof uses class field theory, and a generalization of a well-known theorem of Jordan concerning finite subgroups of \(GL(N)\).

MSC:

11R39 Langlands-Weil conjectures, nonabelian class field theory
11R32 Galois theory
11R42 Zeta functions and \(L\)-functions of number fields
11R37 Class field theory
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