Abstract
We study an analog of Serre's modularity conjecture for projective representations [Formula: see text], where K is a totally real number field. We prove cases of this conjecture when [Formula: see text].
Highlights
Let K be a number field, and consider a continuous representation Ï : GK â GL2(k ), where k is a finite field
Serreâs conjecture and its generalizations assert that any Ï of S type should be automorphic
We say that Ï is of S type if it is absolutely irreducible and totally odd, in the sense that if k has odd characteristic, for each real place v of K, Ï(cv ) is nontrivial
Summary
Let K be a number field, and consider a continuous representation Ï : GK â GL2(k ), where k is a finite field. In this paper we prove new cases of extensions of Serreâs conjecture to mod p representations of absolute Galois groups of totally real number fields.
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