paper

Torsion in abelian fundamental group and its application

arXiv:2501.03431 · doi:10.1093/imrn/rnag052

Abstract

We prove that the torsion subgroup of the abelian fundamental group is finite for a regular geometrically integral projective variety over a local field. We also study the structure of $S K_{1} (X)$ for a regular projective variety $X$ over a local field. As an application, we get class field theory for regular projective curves over local fields.

25 pages, Published in Int. Math. Res. Not. (IMRN)