9 problems

Let $k$ be a flexible field and let $X$ be a smooth projective variety over $k$. Write $\operatorname{CH}_{k/k}(X,\mathbb{Z}/p^m)$ for the isotropic Chow group with…

Let $k$ be a field, and let $\operatorname{Ch}^*_{k/k}$ denote the isotropic Chow groups with $\mathbb{F}_p$-coefficients, obtained from Chow groups by quotienting by classes comin…

Let $X$ be a smooth projective variety of dimension $n$ over $\mathbf{K}$. Let $\|\cdot\|_{\iota}$ denote the chosen operator norm on $\ell$-adic étale cohomology and $\|\cdot\|$ t…

Let $X$ be as above, and let $CH^i(X)^{(0)}$ be the subgroup defined in Proposition 7. Let $CH^i_{\operatorname{num}}(X)$ denote the subgroup of cycles numerically equivalent to…

Let $k$ be a flexible field. The local Chow groups are the groups obtained from the local Chow theory over $k$, while $\operatorname{Ch}^*_{Num}$ denotes Chow groups with…

Numerical triviality conjecture. In $\mathrm{LM}(S)$, $f\sim g$ implies $f=g$; equivalently,

Let $X$ be a smooth projective holomorphic symplectic variety. Write $\operatorname{CH}(X)$ for its Chow ring with rational coefficients and $\overline{\operatorname{CH}}(X)$ for t…

Numerical Chow-group conjecture.

Codimension-one-nef formulation. If