On integral class field theory for varieties over p-adic fields

Let K be a finite extension of the p-adic numbers Qp with ring of integers OK and residue field kappa. Let X a regular scheme, proper, flat, and geometrically irreducible over OK of dimension d, and XK its generic fiber. We show, under some assumptions on X, that there is a reciprocity isomorphism of locally compact groups Har2d-1(XK,Z(d)) <^> 7rab 1 (XK)W from the cohomology theory defined in [10] to an integral model 7rab 1 (XK)W of the abelianized fundamental group 7rab 1 (XK). After removing the contribution from the base field, the map becomes an isomorphism of finitely generated abelian groups. The key ingredient is the duality result in [10]. (c) 2024 Elsevier Inc. All rights reserved.