5 problems

Higher-dimensional Weil conjecture. There exists a $d$-dimensional super lattice model $(V_1,\dots,V_d,R)$ in $\operatorname{Super}_{\mathbb C}$ such that, for every $n\ge 1$, the…

Two-dimensional Weil conjecture. For every endomorphism $M\in\operatorname{End}_{\mathcal C_{\mathbb F_q}}(X)$ there exist super Boltzmann data $(V_1,V_2,R)$ such that, for every f…

Let $X$ be a smooth projective variety of dimension $d$ over the algebraically closed field $\mathbbm{k}$, and let $f$ be a ($q$-)polarized endomorphism of $X$: there is an ample d…

Let $X$ be a smooth projective variety of dimension $n$ over $\mathbf{K}$, and let $f$ be a self-morphism of $X$. Suppose that $f$ is polarized, meaning that … for an ample divisor…

Let $C$ be an algebraic curve over a finite field, and write its zeta function as a rational function of $z=p^{-s}$. Artin's conjecture. Every curve's zeta function satisfies the a…