On algebraic σ-groups
نویسندگان
چکیده
We introduce the categories of algebraic σ-varieties and σ-groups over a difference field (K,σ). Under a “linearly σ-closed” assumption on (K,σ) we prove an isotriviality theorem for σ-groups. This theorem yields immediately the key lemma in a proof of the Manin-Mumford conjecture. The present paper uses crucially ideas from [10] but in a model theory free manner. The applications to Manin-Mumford are inspired by Hrushovski’s work [5] and are also closely related to papers of Pink and Roessler ([11] and [12]).
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تاریخ انتشار 2006