Abstract
We introduce differential arc spaces in analogy to the algebraic arc spaces and show that a differential variety is determined by its arcs at a point. Using differential arcs, we show that if (K,+,×, δ1, . . . , δn) is a differentially closed field of characteristic zero with n commuting derivations and p ∈ S(K) is a regular type over K, then either p is locally modular or there is a definable subgroup G ≤ (K,+) of the additive group having a regular generic type that is nonorthogonal to p.
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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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