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arXiv · 2501.03431

Torsion in abelian fundamental group and its application

Rahul Gupta·Jitendra Rathore
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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 $SK_1(X)$ 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.

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Rahul Gupta, Jitendra Rathore. 2025-01-06. Torsion in abelian fundamental group and its application. https://doi.org/10.1093/imrn%2Frnag052

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