4 problems

Let ${\mathbf H}^{{\mathbb A}^1}_n(X)$ denote the $n$th ${\mathbb A}^1$-homology sheaf of a motivic space $X$, and let $\mathbb G_m$ be the multiplicative group over the base field…

Let $X$ be separated and of finite type over a finite field. Let $H_1^{\operatorname{ar}}(X,\mathbb Z)$ be the first arithmetic homology group, and let $\pi_1^t(X)^{ab}$ denote the…

Let $X$ be a smooth scheme over a finite field, and let $H_i^{KS}(X,\mathbb Z)$ denote Kato-Suslin homology. Generalized integral Kato conjecture. If $X$ is smooth, then … for…

Let $X$ be a smooth scheme over a finite field, and let $H_i^{KS}(X,\mathbb Z)$ denote Kato-Suslin homology. Generalized integral Kato conjecture. If $X$ is smooth, then … for…