7 problems

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 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…

Let $X$ be smooth and proper over a finite field, and let $H^i_{\mathcal M}(X,\mathbb Z(n))$, $H^i_F(X,\mathbb Z(n))$, $H^{i-1}_K(X,\mathbb Z(n))$, and $H^i_W(X,\mathbb Z(n))$ be t…

Let $X$ be a scheme over a finite field, and let $H_i^c(X,\mathbb Z(n))$, $H_i^F(X,\mathbb Z(n))$, and $H_i^K(X,\mathbb Z(n))$ denote the cycle, Weil–étale, and Kato homology group…