4 problems

Serre–Tate l-independence conjecture. The isomorphism classes of these elements of $Rep^{s}(WD_K)$ are all the same, independently of $l$.

Let $K$ be a nonarchimedean local field with residue characteristic $p$, let $X/K$ be a proper smooth variety purely of dimension $n$, let $\sigma \in W_K$, and let…

Let $F$ be a local field of residue characteristic $p>0$, let $X$ be a variety over $F$, and let $\ell\neq p$. By the $\ell$-adic monodromy theorem, one can attach a Weil–Deligne r…

Assume the standard conjectures, and let a motivic Langlands parameter be an isomorphism class of pairs $(T,\kappa)$, where $T$ is a tensor functor from finite-dimensional…