An algebraic proof of Deligne's regularity criterion
| dc.creator | André, Yves | |
| dc.creator | Baldassarri, Francesco | |
| dc.date | 2004-11-24 | |
| dc.date | 2005-01-10 | |
| dc.date.accessioned | 2026-07-07T05:14:40Z | |
| dc.date.available | 2026-07-07T05:14:40Z | |
| dc.description | Deligne's regularity criterion for an integrable connection $\nabla$ on a smooth complex algebraic variety $X$ says that $\nabla$ is regular along the irreducible divisors at infinity in some fixed normal compactification of $X$ if and only if the restriction of $\nabla$ to every smooth curve on $X$ is regular ({\it i. e.} has only regular singularities at infinity). The ``only if" part is the difficult implication. Deligne's proof is transcendental, and uses Hironaka's resolution of singularities. We give here an elementary and purely algebraic proof of this implication: it is, as far as we know, the first algebraic proof of Deligne's regularity criterion. | |
| dc.description | N. Tsuzuki kindly indicated to us a serious error in section 2 of this paper. We think we know a way out, and are working to a revision. Please ignore this manuscript meanwhile! | |
| dc.identifier | https://arxiv.org/abs/math/0411549 | |
| dc.identifier | http://arxiv.org/abs/math/0411549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73361 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | An algebraic proof of Deligne's regularity criterion | |
| dc.type | text |