4 problems

Fix an algebraically closed field $k$ over which resolution of singularities holds, and let $X$ be a scheme of finite type over $k$. For integers $m\geq 1$ and $n\geq 0$, let … be…

Independence-of-prime conjecture. The integer $s_{i,\ell}$ is independent of $\ell$.

Positive-characteristic structure conjecture. There are a uniquely divisible group $V$, integers $s_{i,\ell}$ and $r_i$, and a torsion group…

Correspondence homomorphism conjecture. (i) For any $\alpha\in c_{\mathrm{equi}}(X\times Y/X,0)$, $\mathrm{tr}_{\alpha}$ satisfies (M1). (ii) For any…