3 papers
math.AG2026
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…
math.AG2021
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…
math.AG2020
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…