2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155597In this work, we prove the vanishing of the two cohomological group of the higher local field. This generalize the well-known propriety of finite field and one dimensional local field. We apply this result to study the arithmetic of curve defined over higher local field.Number TheoryAlgebraic Geometry11G25; 14H25text