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On the cohomology of tori over local fields with perfect residue field

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, via Trieste 63, I-35121, Padova, Italy

    Alessandra Bertapelle

  2. Departamento de Matemáticas, Universidad de La Serena, Cisternas 1200, La Serena, 1700000, Chile

    Cristian D. González-Avilés

Authors
  1. Alessandra Bertapelle
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  2. Cristian D. González-Avilés
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Correspondence to Alessandra Bertapelle.

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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

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