Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Grothendieck Duality theories -- abstract and concrete, I:
  pseudo-coherent finite maps   Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor
(-)^! over a suitable category of scheme-maps -- can be developed concretely,
with emphasis on explicit constructions, or abstractly, with emphasis on
category-theoretic considerations. It is not obvious that the two resulting
theories are essentially the same. This is a semi-expository account of the
connection between these approaches, a nontrivial matter involving some
alluring relations, for instance among differential forms, residues and
duality. In particular, it emerges that the culminating Ideal Theorem in
Hartshorne's "Residues and Duality" holds for arbitrary essentially-finite-type
maps of noetherian schemes and bounded-below complexes with quasi-coherent
cohomology. What appears in this first part mostly concerns pseudo-coherent
finite maps. The rest is being prepared.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin