7 papers · 1 filter
Uniform Rost nilpotence and birational motives
David Kumallagov
For a field extension and a Chow motive , let be the base-change ideal. We establ…
Picard groups and composition nilpotence for finite cellular isotropic spectra
David Kumallagov
Let be a flexible field of characteristic different from , let be the mod- isotropic sphere, and set . We prove $$…
Dimension filtrations in birational localisation
David Kumallagov
Let \(S_b\) be the class of birational morphisms between smooth varieties over a field \(F\), and let \(L_n=S_b^{-1}d_{\leq n}\Sm(F)\). Kahn and Sujatha asked whether the natural f…
A coproduct obstruction for derived unramified cohomology
David Kumallagov
Let \(k\) be a perfect field of exponential characteristic \(p\), and let \(R\) be a commutative \(\Z[1/p]\)-algebra. We prove that the first derived unramified functor \[ F\longma…
Smooth weight structures and birationality filtrations on motivic categories
Mikhail V. Bondarko, David Z. Kumallagov
We study various triangulated motivic categories and introduce a vast family of aisles (these are certain classes of objects) in them. These aisles are defined in terms of the corr…
On Chow-weight homology of motivic complexes and its relation to motivic homology
Mikhail V. Bondarko, David Z. Kumallagov
We study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing o…
On Chow weight structures without projectivity and resolution of singularities
Mikhail V. Bondarko, David Z. Kumallagov
In this paper certain Chow weight structures on the "big" triangulated motivic categories are defined in terms of motives of all smooth varieties over the…