4,961 reputation
2936
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 37
visits member for 5 years, 2 months
seen 7 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!

2d
comment Hodge structures generated by cohomology groups of varities with dimension less than $n$
So, $H^{n-1}(X,Q)$ 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 semi-simple.
Jan
27
comment integral p-adic 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
comment 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 Bloch-Kato 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 Bloch-Kato 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 l-adic 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 (non-generic) 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 Bloch-Kato conjecture?
Thank you!! A remark: I suspect that the Mittag-Leffler 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 Bloch-Kato conjecture?
Jan
10
awarded  Enlightened
Jan
10
awarded  Nice Answer
Jan
9
comment 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
comment 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
comment 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).