148 citations · 390 across the 41 of their papers we have counts for
29 papers · 1 filter
Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree
Mikhail V. Bondarko, Kirill S. Ladny, Konstantin I. Pimenov
For a wildly ramified extension of complete discrete valuation fields we study collections of elements of (where ) that fit well for constructing bases of…
Some general étale Weak Lefschetz-type theorems
Sergei I. Arkhipov, Mikhail V. Bondarko
We establish new general etale versions of theorems of Barth and Sommese. Respectively, we compute the lower etale cohomology of closed subvarieties of of small codimensions…
Producing "new" semi-orthogonal decompositions in arithmetic geometry
Mikhail V. Bondarko
This paper is devoted to constructing "new" admissible subcategories and semi-orthogonal decompositions of triangulated categories out of "old" ones. For two triangulated subcatego…
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-pure cohomology and Euler characteristics for motives and varieties, and their relation to unramified cohomology and Brauer groups
Mikhail V. Bondarko
We study Grothedieck groups of triangulated categories using weight structures, weight complexes, and the corresponding pure (co)homological functors. We prove some general stateme…