Torsion in abelian fundamental group and its application

2025/01/06 by Gupta, Rahul, Rathore, Jitendra
#14C35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14G20 #Secondary 14H30

paper · doi:10.48550/arxiv.2501.03431

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 SK₁(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.

Related

• Finiteness properties of torsion fields of abelian varieties
• Torsion of abelian varieties and Lubin-Tate extensions
• Bounds for torsion on abelian varieties with integral moduli
• A Mordell-Weil theorem for abelian varieties over fields generated by torsion points
• Fundamental Group Schemes of some Quot Schemes on a smooth projective\n curve