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The Stacks project

Situation 79.15.3 (Splitting). Let S be a scheme. Let (U, R, s, t, c) be a groupoid scheme over S. Let u \in U be a point. Assume that

  1. s, t : R \to U are separated,

  2. s, t are locally of finite type,

  3. the set \{ g \in G : g\text{ maps to }u\} is finite where G \to U is the stabilizer, and

  4. s is quasi-finite at each point of the set in (3).


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