3 problems

Let $f:\big(\mathbbm{C}^2,0\big)\rightarrow\big(\mathbbm{C}^3,0\big)$ be an injective analytic map germ. The question concerns whether the differential $df(0)$ can have rank less t…

Let $F$ be an analytic map defined in an open neighborhood of $0\in{\mathbb C}^n$, and let $a(z)$ denote the formal series associated with $F$ through the formal differential opera…

Let $Y$ be a $k$-affinoid space, let $X$ be a basic tube, and let $f:X\to Y$ be a weakly analytic map, meaning locally a map of the form $\pi_{K/k}\circ F\circ\sigma_{K/k}$ for a c…