My coauthors and I are writing a paper based on MO questions and answers:
[Friedrich Knop's answer](https://mathoverflow.net/a/237585/4149), 
[my answer 1](https://mathoverflow.net/a/239129/4149)
and
[my answer 2](https://mathoverflow.net/a/239450/4149).
For a linear algebraic group $G$ over a perfect field $k$, I consider a cohomology class $\xi\in H^1(k,G)$. For a finite extension $K/k$, I consider the image of $\xi$ in $H^1(K,G)$, the restriction of $\xi$ to the smaller Galois group.



> 
> **Question.** Is there a standard notation for the image in $H^1(K,G)$ of $\xi\in H^1(k,G)$ ? Is it ${\rm Res}\_k^K(\xi)$ or ${\rm Res}\_K^k(\xi)$ ?
> 
> 
> 


If there is no standard notation, I would be grateful for suggestions of *reasonable* notation.



Notation for the restriction map in Galois cohomology
I've seen both $\text{Res}\_k^K$ and $\text{Res}\_{K/k}$, and similarly for the inflation map if $K/k$ is Galois. More generally, if $\Gamma$ is a group acting on a group $G$ and if $\Lambda\subseteq\Gamma$ is a subgroup, the restriction map $H^1(\Gamma,G)\to H^1(\Lambda,G)$ is commonly written as $\text{Res}^\Gamma\_\Lambda$. 


