All Questions

The Artin reciprocity says that if $$ \chi: \operatorname{Gal}(K/\mathbb Q) \to \mathbb C $$ is a 1-dimensional representation of a finite Galois extension $K/ \mathbb Q$, then it corresponds to a ...

All the papers proving automorphy of the representations of Galois groups of number fields that I have come across seem to first reduce the representation modulo a prime, prove the automorphy of the ...

I wonder why the Artin conjecture is so important. The only reason I could figure out is that one could use the holomorphy of Artin L-series and Weil's converse theorem to show modularity of two-...

Let say you have two number fields, that are tamely ramified, and suppose that the $p$-part of their Dedekind zeta functions coincide for all prime $p$ which is ramified in either field. Suppose ...

This question might be naive and might carry the heuristic that we are living in the best possible world a little too far. If so, I appreciate being told so. Background: Stark's conjecture interprets ...