3 problems

Weil conjecture. The $\ell$-adic component of $\chi(V(K_1))$ is

The horror conjecture. In the language of $T^+$, there are sentences $\tau_{g,p^k,n}$ depending recursively on the parameters such that, for every $g\geq 1$, every prime power…

Let $(F,\operatorname{Frob})\in\mathcal{S}$. For any countable set $A\subseteq F$ and complete quantifier-free $\mathcal{L}_\sigma$-type $p(x)\in S^{qf}_n(A)$, the two dimensions a…