Duality for local fields and sheaves on the category of fields

Duality for complete discrete valuation fields with perfect residue field coefficients in (possibly p-torsion) finite flat group schemes was obtained by Bégueri, Bester, and Kato. In this paper, we give another formulation proof of result. We use the category a Grothendieck topology on it. This simplifies reduces duality to classical results Galois cohomology. A key point is that resulting site correctly captures extension groups between algebraic groups.