6 problems

Let $k$ be a finitely generated field, let $\overline{k}$ be a separable closure, let $\ell$ be different from the characteristic of $k$, let $\Lambda$ be a finite extension of…

Let $\mathbb{F}_q$ be a finite field, and let $Y_0$ and $Z_0$ be varieties over $\mathbb{F}_q$. A morphism $f_0:Z_0\to Y_0$ is $\lambda$-uniform if, for every untwisted compatible…

Let $\mathbb{F}_q$ be a finite field of characteristic $p$, let $X_0$ be a connected normal variety over $\mathbb{F}_q$, let $\ell\ne p$ be a prime, and let $\mathcal{V}_0$ be an i…

Let $C_0$ be a smooth projective curve over the finite field $\mathbb F_q$ of characteristic $p>0$, let $C$ be its base change to $\overline{\mathbb F}_q$, and let $M_K$ and…

Let $\ell$ be a rational prime. Let $X$ be an irreducible regular scheme, flat and of finite type over $\mathbb{Z}[\ell^{-1}]$. Let $E$ be a finite extension of $\mathbb{Q}$, let…

Let $p$ and $\ell$ be distinct primes. Let $X$ be a connected normal scheme of finite type over $\mathbb{F}_p$, and let $\mathcal{E}$ be an irreducible lisse…