For a partial Galois extension of a commutative ring by a finite group, the paper proves that the seven-term sequence 0 to H^1, Pic, PicS, H^2, Brauer group, H^1, H^3 is exact.
Batista, Partial actions: What they are and why we care , Bull
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Partial generalized crossed products and a seven-term exact sequence
For a partial Galois extension of a commutative ring by a finite group, the paper proves that the seven-term sequence 0 to H^1, Pic, PicS, H^2, Brauer group, H^1, H^3 is exact.