NAG

Abstract

We present a Hasse principle for higher-dimensional fields which proves a conjecture of K. Kato. In addition to earlier results we also treat the case of p-torsion in positive characteristic p, asssuming resolution of singularities. Due to recent results on resolution we obtain unconditional results for low dimension. The principal tool is the consideration of weights on cohomology, as initiated in Deligne's proof of the Weil conjectures. The consideration of these weights is less standard for p-torsion in characteistic p.