All Questions

Say a representation $\operatorname{Gal}(\mathbb Q) \to GL_n(\overline{\mathbb Q}_\ell)$ has big monodromy if the Zariski closure of the image of $\operatorname{Gal}(\mathbb Q) $ contains $SO_n$ or $...

The Fontaine-Mazur cojectures says that if $\chi : \text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \to \mathbf{Q}_p^\times$ is a character which is unramified almost everywhere and de Rham at $p$ then it ...

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 ...

Let $F$ be a totally real field. Let $G$ be a (split) connected reductive group over $F$. Let $\pi$ be an irreducible automorphic representation of $G$. Recall in the work of Buzzard and Gee "The ...

Suppose that $R$ is a Noetherian complete domain over a field $K$. Suppose that a monic polynomial $f(X) \in R[X]$ (i.e., the highest degree $X^e$ in $f$ has the coefficient $1$), satisfies the ...