All Questions

Do there exist uncountably many abelian surfaces with good reduction over $\mathbb{Q}_p$ with pairwise non-isomorphic rational $p$-adic Tate modules? If we took $l$-adic Tate modules there would be ...

One can state the generalized Tate conjecture over arbitrary finitely generated fields; to this end one should just define Galois representation to be effective if the eignevalues of the actions of ...

Let $E$ be a number field. For any finite Galois extension $E\subset F$ there is a continuous homomorphism $\pi_F:\mathrm{Gal}(\overline{E}/E)\to \mathrm{Gal}(F/E)$. Let $X$ be a smooth projective ...

Let $M$ be an object of Voevodsky's category $DM_{gm}(K,\mathbb{Q})$ for a number field $K$. For each prime number $\ell$, there is an $\ell$-adic realization $M_{\ell}$ in the bounded derived ...

I think we don't know what crystalline representations come from geometry. What about the unramified ones? Specifically let $\phi:\mathrm{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_p)\to GL_n(\mathbb{Q}...