2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104843We give a criterion for the cohomological dimension of a field, involving norm maps on Milnor K-theory; this criterion was originally formulated by Kato. The theorem we prove is a generalization of a theorem in Serre's book on Galois cohomology.9 pagesK-Theory and HomologyNumber Theorytext