bio  website  buddha239.livejournal.com 

location  St. Petersburg (Russia)  
age  37  
visits  member for  5 years, 2 months 
seen  7 hours ago  
stats  profile views  4,376 
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!
2d

comment 
Hodge structures generated by cohomology groups of varities with dimension less than $n$
So, $H^{n1}(X,Q)$ is a substructure in the corresponding cohomology of a smooth hyperplane section of $X$. Now you should just recall that the category of polarizable (pure) Hodge structures is Abelian semisimple. 
Jan 27 
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integral padic Hodge theory and de Rham representations
This probably means that there exist a certain obstruction to this argument for integral representations. I think that this is also true for the original question: one can try to to construct such a theory (and I know of certain attempts by Breuil, Fontaine, Jannsen, and Zink), but the analogues of certain isomorphisms with rational coefficients are not necessarily isomorphisms integrally (and we can only try to bound the exponents of the "defects"). 
Jan 26 
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Exactness of pure functors
Possibly, you can benefit from Appendix D in users.unimi.it/~barbieri/der1mot.pdf 
Jan 26 
revised 
When does the continuous Galois(=etale) cohomology of fields coincide with the naive one? Often true by the BlochKato conjecture?
added 96 characters in body; edited tags 
Jan 26 
revised 
When does the continuous Galois(=etale) cohomology of fields coincide with the naive one? Often true by the BlochKato conjecture?
added 21 characters in body 
Jan 25 
comment 
Reference for cdh topology
I believe that a proper generically surjective morphism is always surjective. Yet it not clear that above any point $y$ of $Y$ there is an isomorphic point $x$ of $X$ (so, the question is whether the field for $x$ is isomorphic to that for $y$ and not just a finite extension of it). 
Jan 24 
accepted  Continuity of ladic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties? 
Jan 24 
comment 
Reference for cdh topology
Are you sure that all (nongeneric) points of $Y$ lift to $X$? 
Jan 23 
comment 
When does the continuous Galois(=etale) cohomology of fields coincide with the naive one? Often true by the BlochKato conjecture?
Thank you!! A remark: I suspect that the MittagLeffler condition is not an if and only if one. 
Jan 23 
asked  When does the continuous Galois(=etale) cohomology of fields coincide with the naive one? Often true by the BlochKato conjecture? 
Jan 10 
awarded  Enlightened 
Jan 10 
awarded  Nice Answer 
Jan 9 
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Leray's theorem up to some degree
I believe that a slight modification of the "standard" proof would yield the result you want. On the other hand, do you have any specific examples when the corresponding acyclity conditions are fulfilled up to a fixed degree? 
Jan 9 
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Leray's theorem up to some degree
I think that considering the corresponding spectral sequence will give you the answer, whereas this spectral sequence could be found in lots of books. 
Jan 6 
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Why is the CM closure of $\mathbb{Q}$ the “ultimate” coefficient field for motives?
My impression is (I am not an expert in this particular subject) that sometimes one wants to study certain direct summands of motives that are only defined over certain extensions of $Q$. See Remark 4.17 of this paper arxiv.org/abs/0806.3380; you might also try to read the corresponding paper of Scholl. 
Dec 22 
revised 
How would you call a variety that is locally a complete intersection up to defect c?
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Dec 21 
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? 
Dec 21 
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). 