572 research outputs found
On Integral Class field theory for varieties over -adic fields
Let be a finite extension of the -adic numbers with ring
of integers , a regular scheme, proper, flat, and
geometrically irreducible over of dimension , and its generic fiber. We show, under some assumptions on , that
there is a reciprocity isomorphism of locally compact groups
from a new cohomology theory to an integral model of the abelianized geometric fundamental groups . After removing the contribution from the base field, the map
becomes an isomorphism of finitely generated abelian groups
- β¦