Пришел ответ из Advances in Math.
Sep. 24th, 2011 10:02 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
posicСтатья про мотивные пучки Артина-Тейта на гладких многообразиях отвергнута.
"The construction presented here is both clear and original. However, I have reservations concerning its publication. The first one is that I think it lacks corollaries or applications to the motivic theory. The second one is that we would expect a more accurate comparison; ideally a functor from the proposed category of (torsion) Artin-Tate motives to the triangulated category of (torsion) mixed motives. The last one is that I am doubtful concerning the conjecture around which the paper is built, for the following reason.
On Page 2 of the preprint, line 7, the author qualifies the Belinson-Lichtenbaum conjecture - now a theorem, see [Voe11] - as an "etale descent rule". I think this terminology is unfortunate as, on the contrary, this conjecture tells that motivic cohomology with torsion does not satisfy etale descent; moreover, it describes the defect through a truncation. This fact explains my reservation concerning the conjecture of the author: it seems to me that the Artin-Tate motives defined by the author should satisfy etale descent. This would imply more particularly that the Ext groups considered by the author satisfy etale descent - meaning for example that an etale hypercover induces an isomorphism - which should not be true for torsion motivic cohomology.
The material in this paper is quite original but I think it is not yet ready for publication in Advances in Mathematics. In my opinion, the author should try to deepen the line of investigations he has laid down, or may be try a publication in a smaller journal."
Второму замечанию в первом абзаце я как раз собирался последовать (поскольку, по-моему, придумал, как это сделать). Второй абзац -- полный бред, к сожалению (не касаясь терминологического вопроса).
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Из пяти статей, лежавших у меня по редакциям по состоянию на середину марта, две приняты к печати, две отвергнуты, и одна (поданная еще в августе в Crelle's Journal) до сих пор рассматривается.
"The construction presented here is both clear and original. However, I have reservations concerning its publication. The first one is that I think it lacks corollaries or applications to the motivic theory. The second one is that we would expect a more accurate comparison; ideally a functor from the proposed category of (torsion) Artin-Tate motives to the triangulated category of (torsion) mixed motives. The last one is that I am doubtful concerning the conjecture around which the paper is built, for the following reason.
On Page 2 of the preprint, line 7, the author qualifies the Belinson-Lichtenbaum conjecture - now a theorem, see [Voe11] - as an "etale descent rule". I think this terminology is unfortunate as, on the contrary, this conjecture tells that motivic cohomology with torsion does not satisfy etale descent; moreover, it describes the defect through a truncation. This fact explains my reservation concerning the conjecture of the author: it seems to me that the Artin-Tate motives defined by the author should satisfy etale descent. This would imply more particularly that the Ext groups considered by the author satisfy etale descent - meaning for example that an etale hypercover induces an isomorphism - which should not be true for torsion motivic cohomology.
The material in this paper is quite original but I think it is not yet ready for publication in Advances in Mathematics. In my opinion, the author should try to deepen the line of investigations he has laid down, or may be try a publication in a smaller journal."
Второму замечанию в первом абзаце я как раз собирался последовать (поскольку, по-моему, придумал, как это сделать). Второй абзац -- полный бред, к сожалению (не касаясь терминологического вопроса).
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Из пяти статей, лежавших у меня по редакциям по состоянию на середину марта, две приняты к печати, две отвергнуты, и одна (поданная еще в августе в Crelle's Journal) до сих пор рассматривается.
