Definition 42.59.4. Let $(S, \delta )$ be as in Situation 42.7.1. Let $f : X \to Y$ be a local complete intersection morphism of schemes locally of finite type over $S$. We say *the gysin map for $f$ exists* if we can write $f = g \circ i$ with $g$ smooth and $i$ an immersion. In this case we define the *gysin map* $f^! = i^! \circ g^* \in A^*(X \to Y)$ as above.

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