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arXiv · 1903.07010

On line bundles in derived algebraic geometry

Toni Annala
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Abstract

We give examples of derived schemes $X$ and a line bundle $\Ls$ on the truncation $tX$ so that $\Ls$ does not extend to the original derived scheme $X$. In other words the pullback map $\Pic(X) \to \Pic(tX)$ is not surjective. Our examples have the further property that, while their truncations are projective hypersurfaces, they fail to have any nontrivial line bundles, and hence they are not quasi-projective.

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Toni Annala. 2019-03-17. On line bundles in derived algebraic geometry. https://doi.org/10.2140/akt.2020.5.317

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