Remark 59.75.1 (Alternative description of sp). Let $S$, $\overline{s}$, and $\overline{t}$ be as above. Another way to describe the specialization map is to use that

The first equality follows from Theorem 59.53.1 applied to $\text{id}_ S : S \to S$ and the second equality follows from Lemma 59.36.2. Then we can think of $sp$ as the map

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