As you are probably aware, Mathematische Annalen has a policy of publishing articles of high quality, and of general interest (not too specialized); it also operates under strict page quotas. At present, there is also additional pressure on the editors due to a large backlog of accepted articles which have not yet appeared in print; thus increasingly strict standards are applied for acceptance.
The referee liked the paper, but expressed the opinion that the paper was bordeline for Annalen. Here is an extract from the referee's message to me:
``The paper seems interesting. The author proposes a concrete construction of an exact category $F^m_X$ (in his notation) of Artin-Tate motivic sheaves on $X$ with $Z/m$-coefficients. When $X=\Spec(K)$, objects are simply filtered Galois modules $N$ such that ... is a permutational Galois module. (This construction, for $X=\Spec(K)$, is already contained in a previous paper by the author and the extension to a base scheme is quite easy and natural.)
Of course, this construction is primary motivated by the Bloch--Kato conjecture in the form that ...
One main result of the paper is that $F^m_X$ coincides with the smallest full subcategory of $DM(X,Z/m)$ containing relative motives with compact support of finite $X$-schemes (those corresponds to the Artin part) and closed by extension and twists. This is a quite nice result but the proof seems to be essentially a formal consequence of known results.
Another notable result is the construction of a map ... and hence to ... by Bloch--Kato. (The construction of the map is not difficult at all, at least once you know it.)
A very interesting conjecture is that the above map is an isomorphism (a sort of a $K(\pi,1)$-conjecture). A result in the paper reduces this conjecture to the case where $X$ is the spectrum of a field. The $K(\pi,1)$-conjecture goes beyond the Bloch--Kato conjecture. I haven't thought at all about this conjecture myself and it is not clear to me why one should believe it (unless, maybe if $K$ is a number field). [For example, with rational coefficients, the $K(\pi,1)$-property for Tate motives is probably false if the field has non-zero transcendence degree over $Q$. On the other hand, motivic cohomology with rational coefficients and finite coefficients are two quite different things.]
To conclude: I would say that the paper could be considered good enough for Mathematische Annalen (certainly after revision) but, to me, it doesn't stand as a clear case.''
I also note that your paper is over 30 pages long, and with page restrictions and backlog pressures, stricter standards would be applicable to your paper. These are specific concerns of this journal, of course.
I regret that, under these circumstances, we are unable to accept the article for Mathematische Annalen.
With best regards,
Это восьмой подряд отказ из международных научных журналов, который я получаю, начиная с осени 2011 года. Следующей остановкой для этой статьи, думаю я, будет Лондонское матобщество. Кому там надо посылать такую работу -- Байотту? Даймонду? Скоробогатову?