First, I am by no means well-versed on cohomology so I apologize if this is too elementary.
I have been going through some basics of etale cohomology, with my ultimate goal being an understanding of some basic applications. I have gone through the Kummer and Artin-Schreier sequences, and wanted to get an idea for how these sequences can help us classify $\mathbb{Z}/n$ and $\mathbb{Z}/p$ torsors.
I found a short exposition by Artin that said $H^1_{et}(X,\mathbb{G}_m)=Pic(X)$, and this was was labelled as Hilbert 90. This presumably has something to do with $\mathbb{G}_m$ being related to $\mathcal{O}_X^*$. Can someone tell me what the additive version of this is, ie what $H^1_{et}(X,\mathbb{G}_a)$ is equal to? Also if anyone has a reference for this being worked out that would be great as well.
