2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139953We prove that the the kernel of the reciprocity map for a product of curves over a $p$-adic field with split semi-stable reduction is divisible. We also consider the $K_1$ of a product of curves over a number field.14 pagesNumber TheoryAlgebraic Geometry11G45; 14C35, 19F05Class field theory for a product of curves over a local fieldtext