2 problems

Let $k$ be a field, let $x$ be an indeterminate, and let $f\in k[x]^{[n]}$ be a residual coordinate, meaning that it becomes a coordinate modulo $x-c$ for each $c\in k$. Dolgachev–…

Let $A$ be a commutative ring with one, let $A^{[n]}$ be a polynomial ring over $A$, let $a,b\in A^{[n]}$, and let $g\in A^{[n]}[y]$. Coordinate equivalence conjecture. If $A$ is a…