6 problems

Let $A$ be the coordinate ring of a smooth affine curve over a number field $k$. Vaserstein's conjecture. The group $SK_1(A)$ is torsion. This conjecture concerns the structure of…

Let $X(cmathbb{R})\subsetcmathbb{R}^2$ be an affine plane cubic whose projective closure has at least two real points at infinity. The preceding example exhibits pathological behav…

Bracket-width conjecture. The bracket width of $\operatorname{Vec}(C)$ is exactly two.

Width conjecture. For $n\geq 2$, the width of $\operatorname{Vec}(\mathbb{A}^1 \setminus \\{p_1,\dots,p_n\\})$ equals two.

Let $k$ be finitely generated over $\mathbb{Q}$, let $X$ be a smooth geometrically connected curve with smooth completion, and let $\Pi_{X/k}(k)$ denote the set of sections over…

Let $U$ be an affine curve over a field $k$ of characteristic $0$, and let $S_{\pi_1(U/k)}$ be the set of conjugacy classes of sections of its fundamental group exact sequence. A s…