Positive characteristic Manin-Mumford theorem

2003/03/26 by Thomas Scanlon, Scanlon, Thomas
Computer Science · Mathematics · Physics and Astronomy · #03C60 #11U09 #14K12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO) #Nonlinear Waves and Solitons #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.LO #math.NT #msc:03C60 #msc:11U09 #msc:14K12

paper · pdf · doi:10.48550/arxiv.math/0303340

arxiv created 2003/03/26 · openalex publication_date 2003/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic. The proof presented here contains the details of the proof sketched by the author in the article "Diophantine geometry from model theory," BSL 7 (2001) no. 1, 37 - 57; using the model theory of difference fields along the lines of Hrushovski. Algebraic proofs have been presented by Pink & Roessler and Pillay.

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