This research proves finiteness of torsion in abelian fundamental groups, suggesting implications for class field theory.
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.
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Gupta et al. (2026) studied this question.
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