On line bundles in derived algebraic geometry
Copyright policy )On line bundles in derived algebraic geometry
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.
9 pages, comments welcome
Mathematics - Algebraic Geometry, deformation theory, 14F05, Mathematics - K-Theory and Homology, derived algebraic geometry, FOS: Mathematics, Picard group, K-Theory and Homology (math.KT), Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, deformation theory, 14F05, Mathematics - K-Theory and Homology, derived algebraic geometry, FOS: Mathematics, Picard group, K-Theory and Homology (math.KT), Algebraic Geometry (math.AG)
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