An algebraic proof of Deligne's regularity criterion for integrable connections
| dc.creator | André, Yves | |
| dc.date | 2007-01-30 | |
| dc.date.accessioned | 2026-07-07T07:43:53Z | |
| dc.date.available | 2026-07-07T07:43:53Z | |
| 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 fuchsian (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 present a purely algebraic proof of this implication which does not use resolution beyond the case of plane curves. It relies upon a study of the formal structure of integrable connections on surfaces with (possibly irregular) singularities along a divisor with normal crossings. | |
| dc.description | 13 pages. This is a sequel to: [Baldassarri F., Towards an algebraic proof of Deligne's regularity criterion. An informal survey of open problems, Milan J. Math. 73 (2005)], and replaces math.AG/0411549. to appear in RIMS Kokyuroku Bessatsu | |
| dc.identifier | https://arxiv.org/abs/math/0701895 | |
| dc.identifier | http://arxiv.org/abs/math/0701895 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123001 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 14 (primary), 34 (secondary) | |
| dc.title | An algebraic proof of Deligne's regularity criterion for integrable connections | |
| dc.type | text |