Abstract
If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension ≤ 1, our results have a particularly simple form and yield, more generally, isomorphisms between Borovoi’s abelian K-cohomology of a reductive group G over K and the k-cohomology of a certain quotient of the algebraic fundamental group of G.
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Partially supported by PRIN 2010-11 (prot. 20105LL47Y-001).
Partially supported by Fondecyt grant 1120003.
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Bertapelle, A., González-Avilés, C.D. On the cohomology of tori over local fields with perfect residue field. Isr. J. Math. 206, 431–455 (2015). https://doi.org/10.1007/s11856-014-1146-4
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DOI: https://doi.org/10.1007/s11856-014-1146-4