The weight-filtered pp-adic invariant-cycles conjecture

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Let XX be regular, and let Wi−1W_{i-1} denote the indicated weight filtration on the pp-adic étale cohomology groups of the special and geometric generic fibres. Let sp⁡\operatorname{sp} be the étale specialization map. Weight-filtered invariant-cycles conjecture. The map

Wi−1Hi(Xsˉ,Qp)→sp⁡Wi−1Hi(Xηˉ,Qp)IW_{i-1}H^i(X_{\bar s},\mathbb Q_p)\xrightarrow{\operatorname{sp}}W_{i-1}H^i(X_{\bar\eta},\mathbb Q_p)^I

is an isomorphism. The source says this follows by combining the preceding two conjectures and presents it as the resulting conjectural statement for pp-adic étale cohomology.

References

Primary source

Matthias Flach and Baptiste Morin, “On the Weil-étale topos of regular arithmetic schemes”, arXiv:1010.3833 (2010).

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