5,323 reputation
21037
bio website buddha239.livejournal.com
location St. Petersburg (Russia)
age 37
visits member for 5 years, 7 months
seen 13 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!

Jun
29
revised When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun
29
revised When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun
29
revised When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun
29
revised Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
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Jun
29
comment A conservative, non faithful functor between triangulated categories
You are always welcome! Sorry for complicated examples; I have just recalled my own experience with these matters.
Jun
28
comment Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
Yes, such a logical argument should work. Yet I would prefer to avoid it since it is not quite "inner mathematical".
Jun
28
asked Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
Jun
28
revised A conservative, non faithful functor between triangulated categories
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Jun
28
comment A conservative, non faithful functor between triangulated categories
Sorry, I was wrong! In my examples all extensions in the heart become trivial; yet the morphisms do not vanish (for simple reasons). I will correct the answer.
Jun
27
revised A conservative, non faithful functor between triangulated categories
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Jun
27
asked When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
Jun
27
comment A conservative, non faithful functor between triangulated categories
Certainly, these Hodge examples are far from being "the easiest ones"; one can certainly construct much simpler examples of transversal structures (such that the weight complex functor will not be faithful). I believe that it suffices to consider one of Paranjape's "higher" derived categories of filtered vector spaces here.
Jun
27
answered A conservative, non faithful functor between triangulated categories
Jun
27
comment Number of $\mathbb F_p$ points constant mod $p$?
@Jason Starr Thank you! I didn't know that (being not an expert in conditions of this sort).
Jun
26
comment Number of $\mathbb F_p$ points constant mod $p$?
Yet my impression is that the notions rationall connectivity/unirationality/etc. are mostly adapted to smooth projective varieties. Still you certainly may look at "nice compactifications" of your $X$ (and ask whether there exists a compactification with prescribed properties).
Jun
26
comment Number of $\mathbb F_p$ points constant mod $p$?
Yes; this seems to be a very reasonable idea! Yet I have an impressing that testing rational connectivity may be rather hard. So I would be glad to read any your further questions in this direction.:)
Jun
26
comment Number of $\mathbb F_p$ points constant mod $p$?
Yes; varieties whose motives are mixed Tate give one of the "easy pieces of $K_0(Mot_{num})$".
Jun
26
revised Number of $\mathbb F_p$ points constant mod $p$?
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Jun
26
revised Number of $\mathbb F_p$ points constant mod $p$?
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Jun
26
comment Number of $\mathbb F_p$ points constant mod $p$?
Yet my "general" pessimism does not mean that one cannot hope to obtain certain information in special cases (i.e., if $X belongs to a "simple" class of varieties; smooth and affine does not seem to be sufficient here).