Every continuous odd absolutely irreducible two-dimensional 2-adic representation of the absolute Galois group of Q that ramifies at only finitely many finite primes occurs in the full completed varying-weight Hecke algebra at some odd tame level, possibly with auxiliary primes.
Every continuous odd absolutely irreducible two-dimensional 2-adic representation of the absolute Galois group of Q that ramifies at only finitely many finite primes occurs in the full completed varying-weight Hecke algebra at some odd tame level, possibly with auxiliary primes.
Every continuous odd absolutely irreducible two-dimensional 2-adic representation of the absolute Galois group of Q that ramifies at only finitely many finite primes occurs in the full completed varying-weight Hecke algebra at some odd tame level, possibly with auxiliary primes.
If correct, extends completed-Hecke occurrence to all odd absolutely irreducible dyadic representations with finite ramification, including scalar residual cases.
Does every odd, absolutely irreducible dyadic Galois representation with finite ramification occur in a completed Hecke algebra?
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