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intuition about the "section after base-change" for flat descent and exactness of the Amitsur complex
Suppose $A \rightarrow B$ is a faithfully flat map of rings. Then the Amitsur complex is exact:
$0 \rightarrow A \rightarrow B \rightarrow B \otimes_A B \rightarrow \dots$
(the second map is $id \...
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