Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations of intersection homology and perverse sheaves with
  duality over the integers   We provide a generalization of the Deligne sheaf construction of intersection
homology theory, and a corresponding generalization of Poincar\'e duality on
pseudomanifolds, such that the Goresky-MacPherson, Goresky-Siegel, and
Cappell-Shaneson duality theorems all arise as special cases. Unlike classical
intersection homology theory, our duality theorem holds with ground
coefficients in an arbitrary PID and with no local cohomology conditions on the
underlying space. Self-duality does require local conditions, but our
perspective leads to a new class of spaces more general than the Goresky-Siegel
IP spaces on which upper-middle perversity intersection homology is self dual.
We also examine categories of perverse sheaves that contain our
"torsion-sensitive" Deligne sheaves as intermediate extensions.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci