bio | website | buddha239.livejournal.com |
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location | St. Petersburg (Russia) | |
age | 37 | |
visits | member for | 5 years, 7 months |
seen | 13 hours ago | |
stats | profile views | 4,665 |
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 |
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When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun 29 |
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When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun 29 |
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When there exists some “cone” of a morphism of (ind-representable) cohomological functors?
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Jun 29 |
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Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?
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Jun 29 |
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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 |
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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 |
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A conservative, non faithful functor between triangulated categories
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Jun 28 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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Number of $\mathbb F_p$ points constant mod $p$?
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Jun 26 |
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Number of $\mathbb F_p$ points constant mod $p$?
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Jun 26 |
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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). |