bio | website | buddha239.livejournal.com |
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location | St. Petersburg (Russia) | |
age | 37 | |
visits | member for | 4 years, 11 months |
seen | 10 hours ago | |
stats | profile views | 4,288 |
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!
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 |
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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 |
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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?
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Oct 24 |
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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 |
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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?
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Oct 5 |
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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
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Oct 5 |
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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 |
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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 |
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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. |
Oct 5 |
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What can one say about zero-cycle groups for products of Chow motives
Thank you!! I will certainly have a look at the papers you mention anyway. |
Oct 5 |
revised |
What can one say about zero-cycle groups for products of Chow motives
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Oct 5 |
asked | What can one say about zero-cycle groups for products of Chow motives |
Oct 2 |
revised |
Which “concrete” morphisms of varieties and motives induce bijections of their lower Chow groups?
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Oct 1 |
revised |
Which “concrete” morphisms of varieties and motives induce bijections of their lower Chow groups?
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Oct 1 |
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Which “concrete” morphisms of varieties and motives induce bijections of their lower Chow groups?
Yes, this is true; yet I would rather prefer somewhat less general examples.:) |
Oct 1 |
revised |
Which “concrete” morphisms of varieties and motives induce bijections of their lower Chow groups?
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