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Remark 107.5.3. (1) One easily verifies (for example, by using the invariance of the relative dimension of locally of finite type morphisms of schemes under base-change; see for example Morphisms, Lemma 29.28.3) that $\dim _ t(T_ x)$ is well-defined, independently of the choices used to compute it.

(2) In the case that $\mathcal{X}$ is also an algebraic space, it is straightforward to confirm that this definition agrees with the definition of relative dimension given in Morphisms of Spaces, Definition 67.33.1.

Comments (2)

Comment #3415 by David Zureick-Brown on

(1) is missing a parenthesis. \ref{}

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