Remark 15.89.21. Given a differential manifold $X$ with a compact closed submanifold $Z$ having complement $U$, specifying a sheaf on $X$ is the same as specifying a sheaf on $U$, a sheaf on an unspecified tubular neighbourhood $T$ of $Z$ in $X$, and an isomorphism between the two resulting sheaves along $T \cap U$. Tubular neighbourhoods do not exist in algebraic geometry as such, but results such as Proposition 15.89.16, Theorem 15.89.18, and Proposition 15.89.19 allow us to work with formal neighbourhoods instead.

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