5,136 reputation
2937
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 37
visits member for 5 years, 4 months
seen 3 hours ago
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!

11h
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 $g$).
20h
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.
1d
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"?
1d
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?
Mar
16
comment Recollement of multiple $t$-structures
I cannot give an answer until I know which functors and triangulated categories you consider.
Mar
16
comment Recollement of multiple $t$-structures
Definitely no geometry is necessary here; yet could you describe the setting you consider in more detail?
Mar
16
comment Gersten Conjecture for Milnor K-theory
Did you read all Kerz's papers on the subject? As far as I remember, he proposed "correcting" Milnor's K-theory in the case when residue fields are finite.
Mar
16
comment Recollement of multiple $t$-structures
Could you explain what gluing data do you have for your $D_i$? My guess it that $D_i$ should have "well-defined images" in the "glued category" $D$.
Mar
16
comment Récollement of stable $t$-structures
Look at Appendix E5 in webusers.imj-prg.fr/~bruno.kahn/preprints/der1mot.pdf
Mar
10
accepted Motivic integration in positive characteristic: how much is known?
Mar
9
comment On Grothendieck's idea on his Standard Conjecture B
This may be true. At least, in some papers written around 1970 (not by Grothendieck:)) I have met the hope that crystalline cohomology (or, maybe, some other $p$-adic cohomology theory) will yield the proof of the last remaining Weil conjecture.
Mar
6
revised K-theory of coherent sheaves on complex manifolds: references and gamma-filtration?
added 108 characters in body
Mar
6
asked K-theory of coherent sheaves on complex manifolds: references and gamma-filtration?
Mar
5
asked Motivic integration in positive characteristic: how much is known?
Mar
2
comment On Grothendieck's idea on his Standard Conjecture B
Well, this was just a guess; you can write down your own one.
Mar
1
comment When does a perverse sheaf occur in the decomposition theorem?
$j_{!*}L$ occurs in the decomposition of a semi-simple perverse $P$ if and only if $L$ is in the decomposition of $j^*P$.
Feb
28
comment When does a perverse sheaf occur in the decomposition theorem?
Moreover, you can restrict further to the generic point $Spec K$ of $S$. Then it remains to study the corresponding continuous $Q_l$-representations of the Galois group of $K$.