On the Galois and flat cohomology of unipotent algebraic groups over non-perfect fields. (English) Zbl 1122.11021

The main object of the note under review is a connected unipotent group \(G\) defined over a local or global field \(k\) of characteristic \(p>0\). The authors are interested in finiteness and certain local-global properties of the Galois and flat cohomology of \(G\). One should note here the striking contrast to the case of zero characteristic, where the first Galois cohomology of \(G\) is trivial. The results announced in the present note provide sufficient conditions for the first flat cohomology of \(G\) to be infinite and local-to-global criteria for the first Galois cohomology to be trivial. The note contains no proofs.


11E72 Galois cohomology of linear algebraic groups
20G10 Cohomology theory for linear algebraic groups
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