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- W2788266979 abstract "According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum $U_R$ of a local ring $R$ that is a complete intersection of dimension $ge 4$. Dao conjectured a generalization for vector bundles $mathscr{V}$ of arbitrary rank on $U_R$: such a $mathscr{V}$ is free if and only if $mathrm{depth}_R(mathrm{End}_R(Gamma(U_R, mathscr{V}))) ge 4$. We use deformation theoretic techniques to settle Dao's conjecture. We also present examples showing that its assumptions are sharp and draw consequences for splitting of vector bundles on complete intersections in projective space." @default.
- W2788266979 created "2018-03-06" @default.
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- W2788266979 date "2020-07-01" @default.
- W2788266979 modified "2023-10-16" @default.
- W2788266979 title "Grothendieck�Lefschetz for vector bundles" @default.
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- W2788266979 doi "https://doi.org/10.14231/ag-2020-016" @default.
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