Une caractérisation différentielle des faisceaux analytiques cohérents sur une variété complexe
| dc.creator | Pali, Nefton | |
| dc.date | 2003-01-14 | |
| dc.date | 2003-01-15 | |
| dc.date.accessioned | 2026-07-07T04:54:27Z | |
| dc.date.available | 2026-07-07T04:54:27Z | |
| dc.description | We give a generalization, in the context of sheaves, of a classical result of Grothendieck concerning the integrability of connections of type $(0,1)$ over a ${\cal C}^{\infty}$ vector bundle over a complex manifold. We introduce the notion of $\bar{\partial}$-coherent sheaf, which is a ${\cal C}^{\infty}$ notion, and we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves. The principal difficulty of the proof is the solution of a quasi-linear differential equation with standard $\bar{\partial}$ as its principal term. We are able to find a solution of this differential equation, using a rapidly convergent iteration scheme of Nash-Moser type. | |
| dc.description | 35 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301146 | |
| dc.identifier | http://arxiv.org/abs/math/0301146 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66255 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Une caractérisation différentielle des faisceaux analytiques cohérents sur une variété complexe | |
| dc.type | text |