I know two generalizations of Hilbert 90, but I don't if there is a statement that contains both:


### The first statement


Let $K$ be a field, then $H^1(Gal(K), GL\_n(K^{sep}))=0$.


### The second statement


Let $X$ be a scheme, then $H^1(X,\mathbb{G}\_m)=Pic(X)$.


### Question


Is there a nice characterization of $H^1(X,GL\_n)$ (where $GL\_n$ is treated as a sheaf in the etale topology) for a general scheme $X$?



What is the general statement of Hilbert 90?
$H^1$ computed via sheaf cohomology coincides with the Cech $H^1$, which can be interpreted as giving transition functions. In particular, $H^1(X, GL\_n)$ is in bijection with the set of rank $n$ vector bundles on $X$ in the Zariski topology (Theorem 11.4 in Milne's notes on etale cohomology).


