n-Excisive functors, canonical connections, and line bundles on the Ran space
Abstract Let X be a smooth algebraic variety over k. We prove that any flat quasicoherent sheaf on $${\text {Ran}}(X)$$ Ran ( X ) canonically acquires a $$\mathscr {D}$$ D -module structure. In addition, we prove that, if the geometric fiber $$X_{\overline{k}}$$ X k ¯ is connected and admits a smoot...
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| Format: | Article |
| Language: | English |
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Springer International Publishing,
2021-09-20T17:30:22Z.
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| Online Access: | Get fulltext |
| Summary: | Abstract Let X be a smooth algebraic variety over k. We prove that any flat quasicoherent sheaf on $${\text {Ran}}(X)$$ Ran ( X ) canonically acquires a $$\mathscr {D}$$ D -module structure. In addition, we prove that, if the geometric fiber $$X_{\overline{k}}$$ X k ¯ is connected and admits a smooth compactification, then any line bundle on $$S \times {\text {Ran}}(X)$$ S × Ran ( X ) is pulled back from S, for any locally Noetherian k-scheme S. Both theorems rely on a family of results which state that the (partial) limit of an n-excisive functor defined on the category of pointed finite sets is trivial. |
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