4,854 reputation
2835
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 37
visits member for 5 years
seen 1 hour 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!

8h
comment How would you call a variety that is locally a complete intersection up to defect c?
Why not "STLCI"?:) Previously I wrote "LSTCI" instead. Was any abbreviation of this sort used in literature?
13h
asked How would you call a variety that is locally a complete intersection up to defect c?
Dec
11
revised Algebraic equivalence vs linear equivalence
edited tags
Dec
10
comment Etale Realization and Gysin Sequence
This is definitely true for the paper your cite. Yet I believe that the statement you want can be extracted from other papers of Deglise. The alternative author is Ayoub (but I have never read much of him).
Dec
4
answered Etale Realization and Gysin Sequence
Nov
30
awarded  Yearling
Nov
29
revised What problem would you base your mathcoin on?
10x11 is not a square;)
Nov
20
comment What is DAG and what has it to do with the ideas of Voevodsky?
Do you know the paper "K-theory and the bridge from motives to noncommutative motives" sciencedirect.com/science/article/pii/S0001870814003570?
Nov
17
comment Use of derivators to the theory of motives?
I would like to express my own understanding of Adeel's answer. So, when treating motives over a base one considers certain triangulated motivic categories over each base scheme and also several types of connecting functors between these categories. The motivic categories are equipped with canonical models, and some of the connecting functors possess canonical lifts to models; yet some of the types of these functors do not seem to possess canonical lifts of this sort. I would really like to know whether algebraic derivators solve this problem!
Oct
24
comment Any counterexamples known for the Generalized Tate conjecture?
Please, pay attention to the P.S.
Oct
24
revised Any counterexamples known for the Generalized Tate conjecture?
added 194 characters in body
Oct
24
comment Any counterexamples known for the Generalized Tate conjecture?
So, you think that it is not the "ordinary generalized" conjecture that becomes false? Possibly, this is the rignt way to read Milne's claim. Thank you!! you!!
Oct
24
asked Any counterexamples known for the Generalized Tate conjecture?
Oct
13
comment relations between derived categories of ind-A and A
I'm affraid that only the semi-simplicity of $A$ can help here. Otherwise it's quite difficult to compute the $D(indA)$-morphisms FROM an object of $A$ to a shift of an ind-object of $A$; this involves the higher projective limit functors.
Oct
7
revised Which “concrete” morphisms of varieties and motives induce bijections of their lower Chow groups?
added 86 characters in body; edited title
Oct
5
comment What can one say about zero-cycle groups for products of Chow motives
Actually, I have realized that it would be ok to compute the Albanese kernel for the product of a large number of curves with genus bounded by some constant. So, I probably need a certain vanishing result for the corresponding Somekawa's K-groups.
Oct
5
revised What can one say about zero-cycle groups for products of Chow motives
added 84 characters in body
Oct
5
comment About embedding pure motives into the triangulated category of mixed motives and some further questions about motivic cohomology
Also, my impression that the paper math.univ-toulouse.fr/~dcisinsk/DMet.pdf (by Cisinski and Deglise; unfortunately the link does not work at the moment) currently gives more information on \'etale motives that Ayoub's texts.
Oct
5
comment About embedding pure motives into the triangulated category of mixed motives and some further questions about motivic cohomology
My impression is that your question is quite sensitive to the choice of notation, whereas the notation widely varies from paper to paper. So I would recommend you to write explicitly which texts you are trying to read.
Oct
5
comment About embedding pure motives into the triangulated category of mixed motives and some further questions about motivic cohomology
I would rather specify that $L$ becomes $Z(1)[2]$ in Voevodksy's notation. Besides, it seems that Cisinski-Deglise's are now able to describe (relative) motives over characteristic $0$ varieties using the cdh-topology.