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

Let K be a finite extension of the p -adic numbers Q p with ring of integers O K and residue field κ. Let X a regular scheme, proper, flat, and geometrically irreducible over O K of dimension d , and X K its generic fiber. We show, under some assumptions on X , that there is a reciprocity isomorphism of locally compact groups H a r 2 d − 1 (X K , Z (d)) ≃ π 1 a b (X K) W from the cohomology theory defined in [10] to an integral model π 1 a b (X K) W of the abelianized fundamental group π 1 a b (X K). 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]. [ABSTRACT FROM AUTHOR]