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 (...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/132077 |
| 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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