5,176 reputation
21037
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 37
visits member for 5 years, 5 months
seen May 23 at 6:49
I am a professor in St. Petersburg State University. I have several papers on (additive Galois module structure of) local fields, formal groups, and finite group schemes. Currently I am studying Voevodsky's motives and their cohomology. In the process I introduced the notion of a weight structure for a triangulated category; this seems to be an interesting piece of homological algebra (that possibly could be applied to algebraic topology). See http://arxiv.org/abs/0903.0091 for a survey of some of my recent results. You can send me letters to mbondarko gmail.com. In particular, if you answered one of my questions, please tell me how can I mention you in my papers!

May
22
revised On various “extension closures” and “orthogonals” in triangulated categories
added 87 characters in body
May
22
revised On various “extension closures” and “orthogonals” in triangulated categories
added 221 characters in body
May
22
revised On various “extension closures” and “orthogonals” in triangulated categories
added 154 characters in body
May
21
revised On various “extension closures” and “orthogonals” in triangulated categories
edited tags
May
21
comment On various “extension closures” and “orthogonals” in triangulated categories
Certainly, in some cases retract-closures or extension-closures are sufficient to "generate" $E$ starting from a smaller $E'$ that is orthogonal to $D$ (and such that $D$ is the maximal class orthogonal to it). Yet my pseudo-extensions seem to give "more" objects in general.
May
21
revised On various “extension closures” and “orthogonals” in triangulated categories
edited tags
May
21
asked On various “extension closures” and “orthogonals” in triangulated categories
May
19
comment Cycle class map in smooth quasi-projective varieties
This looks rather strange; one usually defines cycle classes only for those cohomology theories that satisfy some sort of the homotopy invariance property (that fails for the cohomology you consider unless $X$ is also proper).
May
12
comment Chow groups of locally trivial affine fibrations
I would prefer to write the right hand side of (4) as $A_k(X)$ (since $X$ does not have to be equi-dimensional); everything else seems to be fine.
May
12
awarded  Civic Duty
May
12
comment Do there exist nontrivial motivic cohomology operations preserving weights?
I doubt this conjecture.:) You probably need more restrictions on "operations" to prove a statement like this.
May
12
revised Do there exist nontrivial motivic cohomology operations preserving weights?
edited tags
Apr
16
comment Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?
A counterexamle in the general case (generalizing the one of Matthias Wendt): if you embedd your category $A$ into $B$ that is closed with respect to countable coproducts (or products) then you kill the whole $K_0(A)$ since $K_0(B)=0$.
Apr
1
comment What should one “do” to “strictify” a triangle of transformations coming from a lax commutative triangle of functors?
The units of my adjunctions in the case when $f,g,h$ admit right adjoints (so that one can compose the units for $f$ and $g$).
Mar
31
comment What should one “do” to “strictify” a triangle of transformations coming from a lax commutative triangle of functors?
Yes; if we fix $f$ and its adjoint then the unit and the counit will be fixed also. Yet I am interested in the case when the adjoint to $f$ is not fixed.
Mar
31
comment What should one “do” to “strictify” a triangle of transformations coming from a lax commutative triangle of functors?
Do you prefer "unit/counit of the adjunction"?
Mar
31
asked What should one “do” to “strictify” a triangle of transformations coming from a lax commutative triangle of functors?
Mar
20
comment Récollement of stable $t$-structures
And certainly the result follows immediately from the "formula" for the glued t-structure.
Mar
19
answered Recollement of multiple $t$-structures
Mar
17
comment Recollement of multiple $t$-structures
No, this was not clarified clearly enough for me to understand it. For which triangulated categories do you consider this "multiple glued" t-structures?