3 problems

Rationality conjecture. If the polynomials $\varphi_i$ have rational coefficients, then

Let $K$ be a topological local field over $\boldsymbol{k}$, and let $\operatorname{Res}^{\mathrm{BT}}_{K / \boldsymbol{k}}:\Omega^n_{K / \boldsymbol{k}}\to\boldsymbol{k}$ be its Be…

Let $K$ be an $n$-dimensional topological local field over $\boldsymbol{k}$. Write $obreakOmega^n{K / boldsymbol{k}}twoheadrightarrowOmega^{n,\mathrm{sep}}{K / boldsymbol{k}}$ for…