I'm quite a newbe in the field of motives & A1 homotopy theory,
so please forgive me if the question is too elementary:


In the intro from [wikipedia on Nisnevish topology](https://en.wikipedia.org/wiki/Nisnevich_topology)
is remarked that it's founder Yevsey Nisnevich was originally motivated
by the theory of adeles.


Could somebody elaborate which features/ nuances in
the development of Nisnevich topology
reflect the striking influence on it
by the theory of adeles as stated there?



Nisnevich topology inspired by Adeles
He used the topology to give a cohomological interpretation of the class group/set $c(G)$ of an affine algebraic group (which is defined in terms of adeles, see below), and then to partially prove the Grothendieck-Serre conjecture. I quote Nisnevich's summary of section 2 of his thesis.


2.1. The principal role in the proofs of all results of the thesis is played by a direct relationship between the two kinds of invariants mentioned above: the arithmetic and cohomological invariants for a general affine group scheme $G$.


The idea of such relationships already appeared in the classical isomorphism $$H^{1}(X\_{Zar},\mathbb{G}\_{m,X})\simeq\mathrm{Pic}(\mathbb{G}\_{m,X})=c(\mathbb{G}\_{m,X}),$$ which was generalized by Voskresenky and Harder to some other groups $G$. Unfortunately, in general [the] Zariski topology on $X$ is too weak to give a description of $c(G)$ and other arithmetic invariants and properties of $G$. To describe them one needs a stronger topology on $X$. For these purposes an appropriate topology is in introduced in Ch. I of the thesis. To use the topology in Ch. IV-V we define it in the following more general situation.


2.2. Let $R$ be a one dimensional regular ring, $k$ the field of fractions of $R$, $X=\mathrm{Spec}\,R$, $A$ and $A(X)$ the ring of adeles and $X$-integral adeles of $X$, $G$ an affine group scheme over $X$ with smooth general fibre $G\otimes\_{R}k$, $c(G)=G(A(X))\backslash G(A)/G(k)$ the set of double cosets of $G(A)$, or in the case when $c(G)$ is a group, the class group of $G$.


2.3 Theorem-definition. There exists a Grothendieck topology $X\_{cd}$ on $X$ (we shall call it the completely decomposed topology) for which one has a canonical bijection $$\alpha(G)\colon H^{1}(X\_{cd},G)\simeq c(G).$$


