$X{\otimes}_AK$ is normal, Section \[11.04.2019–4\] explains how to obtain information about $\Pi(X,{\varphi},x_0){\otimes}_AK$ from the category of essentially finite vector bundles (as defined [@nori]) on $X{\otimes}_AK$. See Theorem \[11.04.2019–2\] and Corollary \[16.04.2019–1\].

Section \[14.03.2019–1\] studies ${\mathfrak{T}}_{\varphi}$ by means of an idea introduced in [@hai-dos_santos18]. In this work, we found a property of representations of a flat and affine group scheme $G$ over a complete $A$, called prudence, which allows us to verify when the $A$-module of functions $A[G]$ is free. This is particularly pleasing for the present theory since, on the geometric side, prudence is roughly Grothendieck’s algebraization. This fact allows us to show that the full Galois groups constructed from ${\mathfrak{T}}_{\varphi}$ are in many cases [*finite*]{} group schemes, see Corollary \[25.06.2018–2\]. In doing so, we provide an argument to substantiate a claim made in Lemma 3.1 and Theorem 4.1 of [@mehta-subramanian13]. (See also our summary of Section \[06.03.2019–1\] below.)

Section \[RFT\] recalls the reduced fibre theorem and puts it in a way which can conveniently be employed in the rest of the work, see Theorem \[reduced\_fibre\_theorem\]. Note that, this powerful theorem comes with the (mild) hypothesis that a certain generic fibre should be geometrically reduced; since we wish to profit 