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

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,...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 206; no. 1; pp. 431 - 455
Main Authors Bertapelle, Alessandra, González-Avilés, Cristian D.
Format Journal Article
LanguageEnglish
Published Heidelberg The Hebrew University Magnes Press 01.02.2015
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Exact Sequence
Short Exact Sequence
Abelian Group
Canonical Isomorphism
Cohomological Dimension
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Summary: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 .
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-014-1146-4