Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recollements of derived categories I: Exact contexts   Recollements were introduced originally by Beilinson, Bernstein and Deligne
to study the derived categories of perverse sheaves, and nowadays become very
powerful in understanding relationship among three algebraic, geometric or
topological objects. The purpose of this series of papers is to study
recollements in terms of derived module categories and homological ring
epimorphisms, and then to apply our results to both representation theory and
algebraic K-theory.
  In this paper we present a new and systematic method to construct
recollements of derived module categories. For this aim, we introduce a new
ring structure, called the noncommutative tensor product, and give necessary
and sufficient conditions for noncommutative localizations which appears often
in representation theory, topology and K-theory, to be homological. The input
of our machinery is an exact context which can be easily obtained from a rigid
morphism that exists in very general circumstances. The output is a recollement
of derived module categories of rings in which the noncommutative tensor
product of an exact context plays a crucial role. Thus we obtain a large
variety of new recollements from commutative and noncommutative localizations,
ring epimorphisms and extensions.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con