On the topology on group cohomology of algebraic groups over complete valued fields (Q397879)

Given a linear algebraic group \(G\) over a field \(k\) which is complete with respect to a non-trivial valuation of real rank \(1\), the authors define two topologies on the flat cohomology sets \(H^1_{\mathrm{flat}}(k,G)\) -- the \textit{special} topology and the \textit{canonical} topology -- and show that these topologies coincide. The special topology is defined via an embedding of \(G\) into a so-called \textit{special} group, but the authors also show that it is independent of such an embedding. The results also hold over the adèle ring of a global field.