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# A Hodge-Type Filtration on Rigid Cohomology

Mar 2023

Given a scheme X over a complete discrete valuation ring ${\mathcal O}_K$ ofmixed characteristic,Gros,in his study of syntomic cohomology in the smooth andproper case, introduced a filtration on the rigid cohomology of the specialfiber $X_k$.Gros claimed that this construction was independent of the choiceof immersions involved, citing an unpublished paper of Berthelot. However noproofs of this have appeared: here we prove it.

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