I encountered the Hochschild-Serre spectral sequence in étale cohomology
$$H^i(\text{Gal}(\overline{k}/k), H^j_{et}(X_{\overline{k}}, F))\Rightarrow H^{i+j}_{et}(X_{{k}}, F)$$
How is the filtration on $H^*_{et}(X_{{k}}, F)$ "associated to the Hochschild-Serre spectral sequence" defined? Several authors quote it without ever defining it.
Is $F^aH^*$ the image, or a union of images, of differentials in the spectral sequence?
Could you give a reference where the induced filtration on the Hochschild -Serre spectral sequence is explained?
Example What is $F^1H^n(X_k, F)\subset H^1(\text{Gal}(\overline{k}/k), H^{n-1}(X_{\overline{k}}, F))$ ?
