Post 11: Correction to Perverse Sheaves Part 4

10 Jan 2024

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You don’t need to read this post if you read Part 4 after January 10 2024.

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I mistakenly said that the bounded variants of $Ch(\mc A)$ and $K(\mc A)$ are defined by conditions on the cohomology of objects. However, it should instead be conditions on the complexes themselves. In particular:

• $Ch^+(\mc A)$ and $K^+(\mc A)$ consist of complexes $A^\bullet$ for which there is an integer $N$ such that $A^i=0$ for $i< N$.

• $Ch^-(\mc A)$ and $K^-(\mc A)$ consist of complexes $A^\bullet$ for which there is an integer $N$ such that $A^i=0$ for $i > N$.

• $Ch^b(\mc A)$ and $K^b(\mc A)$ consists of complexes $A^\bullet$ for which there is a positive integer $N$ such that $A^i=0$ for $|i| > N$.