Lemma 49.6.2. Let $A \to B$ be a finite type ring map. Let $A \to A'$ be a flat ring map. Set $B' = B \otimes _ A A'$.

The annihilator $J'$ of $\mathop{\mathrm{Ker}}(B' \otimes _{A'} B' \to B')$ is $J \otimes _ A A'$ where $J$ is the annihilator of $\mathop{\mathrm{Ker}}(B \otimes _ A B \to B)$.

The Noether different $\mathfrak {D}'$ of $B'$ over $A'$ is $\mathfrak {D}B'$, where $\mathfrak {D}$ is the Noether different of $B$ over $A$.

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