Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative (crepant) desingularizations and the global spectrum of
  commutative rings   In this paper we study endomorphism rings of finite global dimension over not
necessarily normal commutative rings. These objects have recently attracted
attention as noncommutative (crepant) resolutions, or NC(C)Rs, of
singularities. We propose a notion of a NCCR over any commutative ring that
appears weaker but subsumes all previous notions. Our results yield strong
necessary and sufficient conditions for the existence of such objects in many
cases of interest. We also give new examples of NCRs of curve singularities,
regular local rings and normal crossing singularities. Moreover, we introduce
and study the global spectrum of a ring $R$, that is, the set of all possible
finite global dimensions of endomorphism rings of MCM $R$-modules. Finally, we
use a variety of methods to compute global dimension for many endomorphism
rings.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th