4,403 reputation
1531
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 36
visits member for 4 years, 4 months
seen 35 mins 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!

2h
asked Comparison of K-groups of (affine) singular schemes with K'=G-groups
Apr
2
awarded  Nice Answer
Mar
27
comment The link between the subfactors and the motives as enriched Galois theories?
One of the basic ideas for motives is that they shouldn't be closey related with any particular topos.
Mar
25
comment Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
Thank you; I should think about this. Is this $lim^1$ often non-trivial? Actually, I could formulate my question more vaguely: could one express $\varinjlim H^\ast_{et}(X_i, \mathbb{Z}_l)$ 'reasonably' in terms of some cohomology of $\eta$?
Mar
24
revised Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
added 116 characters in body
Mar
24
comment Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
Thank you!! I corrected my question; one should consider the $l$-adic completion of the limit in question. About your second remark: surely, the image of Gysin could kill a part of the cohomology of $X$; yet my idea was to prove that for any 'small enough' $X_i$ its cohomology injects into the one of $\eta$.
Mar
24
revised Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
One should consider the l-adic completion of the limit of $H^\ast_{et}(X_i, \mathbb{Z}_l)$ instead of the limit itself in my question.
Mar
24
revised Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
added 208 characters in body
Mar
24
asked Continuity of l-adic cohomology: is the cohomology of the generic point isomorphic to the completion of the limit of cohomology of open subvarieties?
Mar
10
comment Chow ring of two varieties
This is very far from being elementary!:) No general answer is possible.
Mar
3
comment $p$-adic periods
Hodge-Tate decompositions yield non-trivial periods in $C_p$. Fontaine's mysterious functor yields periods in $B_{st}$. Why do you want periods in $Q_p$?
Feb
14
revised The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)
edited tags
Feb
14
awarded  Nice Question
Feb
14
revised The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)
added 45 characters in body
Feb
14
asked The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)
Feb
8
answered Applications of homotopy purity theorem of Morel-Voevodsky
Jan
25
revised Vanishing cycles of a locally constant sheaf for a smooth morphism in the $l = p$-case
edited tags
Jan
25
revised Is there a good way to think of vanishing cycles and nearby cycles?
edited tags
Jan
25
revised Higher vanishing cycles
edited tags
Jan
25
revised The Rappoport-Zink spectral sequence vs. the one of the complement of a normal crossing divisor
added 142 characters in body; edited tags