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arXiv · 2312.09438

A Beauville-Laszlo-type descent theorem for locally Noetherian schemes

Robin Louis
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Abstract

Let $X$ be a locally Noetherian scheme with a closed subscheme $Z$. Let $\mathcal{X}$ be the completion of $X$ at $Z$, considered as a formal scheme. We show that a coherent sheaf on $X$ is equivalently given by a coherent sheaf on $\mathcal{X}$, a coherent sheaf on the complement of $Z$, and an isomorphism of pullbacks of these sheaves to a certain adic space $W$. By defining $W$ as an adic space instead of as a Berkovich space we are able to generalize the descent result of Ben-Bassat and Temkin from finite type $k$-schemes to locally Noetherian schemes.

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Robin Louis. 2023-11-02. A Beauville-Laszlo-type descent theorem for locally Noetherian schemes. https://arxiv.org/abs/2312.09438

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