Torsion in Abelian Fundamental Group and Its Application

Key Points

• To establish the finiteness of the torsion subgroup of the abelian fundamental group and explore its implications.
• Proved the torsion subgroup's finiteness for regular geometrically integral projective varieties over local fields.
• Analyzed the structure of SK1(X) for regular projective varieties X over local fields.
• Investigated applications related to class field theory for regular projective curves.
• Demonstrated that torsion subgroup is finite for specific projective varieties.
• Found structural insights into SK1(X) related to local fields.
• Derived class field theory results for regular projective curves over local fields.