Gabber's torsion-freeness conjecture for punctured spectra

Let (R,m)(R,\mathfrak{m}) be a local complete intersection ring of dimension 33. Let

UR=Spec(R){m}U_R=\operatorname{Spec}(R)-\{\mathfrak{m}\}

be the punctured spectrum of RR. Gabber's conjecture. The group Pic(UR)\operatorname{Pic}(U_R) is torsion-free. The paper notes that its positive-characteristic case follows from the theorem proved there; the conjecture is attributed to Gabber and concerns the absence of torsion in Picard groups of punctured spectra of three-dimensional local complete intersections.

Sources & referencesView supporting material

Primary source

Hailong Dao and Ilya Smirnov, “On generalized Hilbert-Kunz function and multiplicity”, arXiv:1305.1833 (2019).

Additional references

3 papers in this index state this conjecture (2009–2013). The statement above is taken from the most recent of them; the others are arXiv:1004.0471, arXiv:0911.4268.

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