n-Excisive functors, canonical connections, and line bundles on the Ran space
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Author(s)
Tao, James
Date Issued
January 5, 2021
Publisher
Springer International Publishing
Citation
Selecta Mathematica. 2021 Jan 05;27(1):2
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00029-020-00611-4
