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arXiv · 1906.07976

$n$-excisive functors, canonical connections, and line bundles on the Ran space

James Tao
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Abstract

Let $X$ be a smooth algebraic variety over $k$. We prove that any flat quasicoherent sheaf on $\operatorname{Ran}(X)$ canonically acquires a D-module structure. In addition, we prove that, if the geometric fiber $X_{\overline{k}}$ is connected and admits a smooth compactification, then any line bundle on $S \times \operatorname{Ran}(X)$ 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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James Tao. 2019-06-19. $n$-excisive functors, canonical connections, and line bundles on the Ran space. https://arxiv.org/abs/1906.07976

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