Global rigid inner forms vs isocrystals (Q6052101)

In the paper under the review, the authors compare the cohomology of two global Galois gerbes, which is an integral part of Arthur-Langlands conjectures for non-quasi-split reductive groups. These gerbes lead to the so-called isocrystal and rigid versions of the refined local Langlands conjectures. As the first application, the authors compare the normalized local pairings at each place of a finite extension \(F\) of \(\mathbb{Q}\). As the second application, authors reprove that the product of local normalized transfer factors equal the canonical adelic transfer factor, under a weaker hypothesis.