Katz–Lang finiteness theorem
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Short description: On kernels of maps between abelianized fundamental groups of schemes and fields
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In number theory, the Katz–Lang finiteness theorem, proved by Nick Katz and Serge Lang (1981), states that if X is a smooth, geometrically connected scheme of finite type over a field K that is finitely generated over the prime field, and Ker(X/K) is the kernel of the maps between their abelianized fundamental groups, then Ker(X/K) is finite if K has characteristic 0, and the part of the kernel coprime to p is finite if K has characteristic p > 0.
References
- Katz, Nicholas M.; Lang, Serge (1981), With an appendix by Kenneth A. Ribet, "Finiteness theorems in geometric classfield theory", L'Enseignement Mathématique, IIe Série 27 (3): 285–319, doi:10.5169/seals-51753, ISSN 0013-8584
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