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A cohomology class of a smooth complex variety of dimension $n$ has coniveau $geq c$ if it vanishes in the complement of a closed subvariety of codimension $geq c$, and has strong coniveau $geq c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $leq n-c$. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties.
We construct and study a scheme theoretical version of the Tits vectorial building, relate it to filtrations on fiber functors, and use them to clarify various constructions pertaining to Bruhat-Tits buildings, for which we also provide a Tannakian description.
We define and study Harder-Narasimhan filtrations on Breuil-Kisin-Fargues modules and related objects relevant to p-adic Hodge theory.
We construct a triangulated analogue of coniveau spectral sequences: the motif of a variety over a countable field is decomposed (in the sense of Postnikov towers) into the twisted (co)motives of its points; this is generalized to arbitrary Voevodsky
We define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate these construc
We demonstrate that a conjecture of Teh which relates the niveau filtration on Borel-Moore homology of real varieties and the images of generalized cycle maps from reduced Lawson homology is false. We show that the niveau filtration on reduced Lawson