Turner's simplicial vanishing conjecture for local complete intersections

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Let F\Bbb{F} be a field and let RR be a simplicial commutative ring that is locally finite and locally of non-zero characteristic. Say that RR is locally a complete intersection when each localization R℘R_{\wp} is a complete intersection, and that it is locally QQ-bounded when (Qπ∗R℘)s=0(Q\pi_*R_{\wp})_s=0 for all sufficiently large ss at every simplicial prime ideal ℘\wp. Turner's vanishing conjecture. RR is locally a complete intersection if and only if RR is locally QQ-bounded. This is proposed as a simplicial generalization of Quillen's conjecture. The source proves the conjecture under the stated finite-type and non-zero-characteristic hypotheses, while the general simplicial formulation is presented as the proposed statement.

References

Primary source

James M. Turner, “On Simplicial Commutative Rings with Vanishing André-Quillen Homology”, arXiv:alg-geom/9707018 (1997).

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