Let k be a field of positive characteristic p with degree of imperfection 1 and a nontrivial discrete valuation. We show that the Galois and flat cohomology of unipotent k-groups over k of dimension are finite (in fact, trivial) if and only if they are k-split. We give some examples to show that the bound is best possible and present several applications to local-global principles.
"On the Galois and Flat Cohomology of Unipotent Algebraic Groups over Local and Global Function Fields. II." Michigan Math. J. Advance Publication 1 - 21, 2023. https://doi.org/10.1307/mmj/20216162