Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stratifications of derived categories from tilting modules over tame
  hereditary algebras   In this paper, we consider the endomorphism algebras of infinitely generated
tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame
hereditary $k$-algebras $R$ with $k$ an arbitrary field, where
$R_{\mathcal{U}}$ is the universal localization of $R$ at an arbitrary set
$\mathcal{U}$ of simple regular $R$-modules, and show that the derived module
category of $\End_R(R_{\mathcal U}\oplus R_{\mathcal U}/R)$ is a recollement of
the derived module category $\D{R}$ of $R$ and the derived module category
$\D{{\mathbb A}_{\mathcal{U}}}$ of the ad\`ele ring ${\mathbb A}_{\mathcal{U}}$
associated with $\mathcal{U}$. When $k$ is an algebraically closed field, the
ring ${\mathbb A}_{\mathcal{U}}$ can be precisely described in terms of Laurent
power series ring $k((x))$ over $k$. Moreover, if $\mathcal U$ is a union of
finitely many cliques, we give two different stratifications of the derived
category of $\End_R(R_{\mathcal U}\oplus R_{\mathcal U}/R)$ by derived
categories of rings, such that the two stratifications are of different finite
lengths.

16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg