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Apr
22
revised motives wiki description
I do not understand some of the sentences in this text. Currently I have corrected the claim that no definition of mixed motives exists (since there are Nori motives and Voevodsky motives whose \'etale cohomology is concentrated in degree zero).
Apr
22
awarded  Tag Editor
Apr
22
revised motives wiki excerpt
I do not understand some of the sentences in this text. Currently I have corrected the claim that no definition of mixed motives exists (since there are Nori motives and Voevodsky motives whose \'etale cohomology is concentrated in degree zero).
Apr
22
suggested approved edit on motives tag wiki
Apr
22
suggested approved edit on motives tag wiki excerpt
Apr
21
comment When may “summand of” be dropped from the definition of perfect dg module?
Unfortunately I have never studied this setting. I beiieve that Orlov, Luntz, Efimov and others are the authors who have studied it in detail.
Apr
21
revised Big list - Equivalent descriptions of Hodge conjecture?
deleted 5 characters in body; edited tags
Apr
21
asked Do closed points have “locally maximal” codimensions?
Apr
20
awarded  Nice Question
Apr
15
comment When may “summand of” be dropped from the definition of perfect dg module?
You may have a look at section 1.5.6 in Beilinson's math.harvard.edu/~gaitsgde/grad_2009/motvo.pdf.
Apr
15
comment Uniqueness of smooth compactification upto a smooth morphism
I have several papers on this subject (arxiv.org/find/math/1/au:+Bondarko_M/0/1/0/all/0/1) including the survey arxiv.org/abs/0903.0091 that is unfortunately far from being perfect. If you don't like my style and/or Voevodsky motives then you can also read the (somewhat "classical") paper Gillet H., Soulé C. Descent, motives and K-theory// J. reine und angew. Math. 478, 1996, 127–176.
Apr
14
comment Non-uniqueness of smooth compactification
Dear Sandor: yes, you are quite right. I have have just meant that a significant generalization of this result is now available.
Apr
14
comment Uniqueness of smooth compactification upto a smooth morphism
So, it seems that your question is not a "right" one. Are you interested in other results in this direction (say, in motivic or cohomological ones)?
Apr
14
comment Non-uniqueness of smooth compactification
Sorry for not noticing your comment earlier.:) The answer is that weight complexes are functorial up to homotopy, and weight spectral sequences are functorial starting from $E_2$ for any (co)homology theory that factors through motives..
Apr
9
awarded  Nice Question
Apr
8
answered The vanishing of $MGL^{2n+i,n}(X)$; do spectra of smooth projective varieties generate $SH_{l}$?
Apr
7
comment Intuition behind the definition of finite correspondences
I would rather say that you cannot define Voevodsky motives if you move cycles since you want to treat correspondences instead of their rational equivalence classes. The possibility to treat singular schemes is just a bonus here.
Mar
24
revised Does the numerical equivalence relation coincide with the homological one for 1-cycles (in positive characteristic)?
edited title
Mar
22
accepted For a finite flat (etale?) morphism $f:Y\to X$, is $f_*1_Y-\deg f . 1_X$ nilpotent in $A^0(X)$, where $A^*$ is the algebraic cobordism?
Mar
16
comment Does the numerical equivalence relation coincide with the homological one for 1-cycles (in positive characteristic)?
Thanl you! So, the general case of the statement is not known at the moment.