Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two finiteness theorem for $(a,b)$-module   We prove the following two results
  1. For a proper holomorphic function $ f : X \to D$ of a complex manifold
  $X$ on a disc such that $\{df = 0 \} \subset f^{-1}(0)$, we construct, in a
functorial way, for each integer $p$, a geometric (a,b)-module $E^p$ \
associated to the (filtered) Gauss-Manin connexion of $f$.
  This first theorem is an existence/finiteness result which shows that
geometric (a,b)-modules may be used in global situations.
  2. For any regular (a,b)-module $E$ we give an integer $N(E)$, explicitely
given from simple invariants of $E$, such that the isomorphism class of
$E\big/b^{N(E)}.E$ determines the isomorphism class of $E$.
  This second result allows to cut asymptotic expansions (in powers of $b$) \
of elements of $E$ without loosing any information.

27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
9
The categories of this paper are: nlin