Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight structures vs. $t$-structures; weight filtrations, spectral
  sequences, and complexes (for motives and in general)   This paper is dedicated to triangulated categories endowed with weight
structures (a new notion; D. Pauksztello has independently introduced them as
co-t-structures). This axiomatizes the properties of stupid truncations of
complexes in $K(B)$. We also construct weight structures for Voevodsky's
categories of motives and for various categories of spectra. A weight structure
$w$ defines Postnikov towers of objects; these towers are canonical and
functorial 'up to morphisms that are zero on cohomology'. For $Hw$ being the
heart of $w$ (in $DM_{gm}$ we have $Hw=Chow$) we define a canonical
conservative 'weakly exact' functor $t$ from our $C$ to a certain weak category
of complexes $K_w(Hw)$. For any (co)homological functor $H:C\to A$ for an
abelian $A$ we construct a weight spectral sequence $T:H(X^i[j])\implies
H(X[i+j])$ where $(X^i)=t(X)$; it is canonical and functorial starting from
$E_2$. This spectral sequences specializes to the 'usual' (Deligne's) weight
spectral sequences for 'classical' realizations of motives and to
Atiyah-Hirzebruch spectral sequences for spectra. Under certain restrictions,
we prove that $K_0(C)\cong K_0(Hw)$ and $K_0(End C)\cong K_0(End Hw)$.
  The definition of a weight structure is almost dual to those of a
t-structure; yet several properties differ. One can often construct a certain
$t$-structure which is 'adjacent' to $w$ and vice versa. This is the case for
the Voevodsky's $DM^{eff}_-$ (one obtains certain new Chow weight and
t-structures for it; the heart of the latter is 'dual' to $Chow^{eff}$) and for
the stable homotopy category. The Chow t-structure is closely related to
unramified cohomology.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin