Two finiteness theorem for $(a,b)$-module
| dc.creator | Barlet, Daniel | |
| dc.date | 2008-01-28 | |
| dc.date.accessioned | 2026-07-07T08:56:51Z | |
| dc.date.available | 2026-07-07T08:56:51Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0801.4320 | |
| dc.identifier | http://arxiv.org/abs/0801.4320 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146759 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32S05 ; 32S20 ; 32S25 ; 32S40 | |
| dc.title | Two finiteness theorem for $(a,b)$-module | |
| dc.type | text |