A positive characteristic Manin–Mumford theorem

2005/11/01 by Thomas Scanlon · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.1112/s0010437x05001879

Abstract

We present the details of a model-theoretic proof of an analogue of the Manin–Mumford conjecture for semiabelian varieties in positive characteristic. As a by-product of the proof we reduce the general positive-characteristic Mordell–Lang problem to a question about purely inseparable points on subvarieties of semiabelian varieties.

Cited by

• Survey on the geometric Bogomolov conjecture
• Positivity of Hodge bundles of abelian varieties over some function fields
• On p-adic versions of the Manin-Mumford Conjecture

Related

• Positive characteristic Manin-Mumford theorem
• Around the Mordell-Lang and Manin-Mumford conjectures in positive characteristic
• On the Manin-Mumford and Mordell-Lang conjectures in positive characteristic
• A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic
• The Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic