Takashi Suzuki
Published 2013-10-18, updated 2015-04-23Version 3
Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of this result. We use the category of fields and a Grothendieck topology on it. This simplifies the formulation and proof and reduces the duality to classical results on Galois cohomology. A key point is that the resulting site correctly captures extension groups between algebraic groups.
Comments: 53 pages. Revised following the referee's comments
On the cohomology of tori over local fields with perfect residue field
On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields
Invitation to higher local fields, Part I, section 14: Explicit abelian extensions of complete discrete valuation fields
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