10 problems

Weil–étale order-of-vanishing conjecture.

Kahn's conjecture. For every prime $l$ and any $i$, the map $c$ induces an isomorphism

Beshenov's special-value conjecture. The special value $\zeta^*(X,n)$ is determined up to sign by

Let $X$ be an arithmetic scheme and let $n<0$ be an integer. Assume that $\zeta(X,s)$ has a meromorphic continuation around $s=n$, and let $H^i_{\mathrm{W,c}}(X,\mathbb{Z}(n))$ den…

Let $X$ be an arithmetic scheme such that $X_{\mathbb{C}}$ is smooth and quasi-projective, and let $n<0$. Let $G_{\mathbb{R}}=\operatorname{Gal}(\mathbb{C}/\mathbb{R})$, let…

Let $X$ be a regular arithmetic scheme and let $r$ be an integer. Define … where $\lambda^q\Omega_{X/\mathbb{Z}}$ denotes the derived exterior power. De Rham-to-Weil–étale map conj…

Let $X$ be regular, projective, and flat over $\operatorname{Spec}\mathbb{Z}$, and let $r$ be an integer. Let $\mathbb{Z}(r)$, $\mathbb{Z}_B^+(r)$, and $t(r)$ be the corresponding…

The Weil–étale motivic cohomology groups are cohomology groups on the Weil–étale site, and the cohomology groups of sheaves of differentials are finite. Finite-generation conjectur…

Let $X$ be a smooth projective variety over the finite field $\q$ with $q$ elements, let $Z(X,t)$ be its zeta function, let $n$ be an integer, let $\rho_n$ denote the relevant orde…

Let $X$ be smooth and projective over a finite field, and let $C_i(X)$ be the homology groups of the complex $KC_1^{F\operatorname{et}}(X)$ measuring the difference between Weil–ét…