Canonical integral structures on the de Rham cohomology of curves
| dc.creator | Cais, Bryden | |
| dc.date | 2008-06-16 | |
| dc.date | 2009-03-17 | |
| dc.date.accessioned | 2026-07-07T12:53:00Z | |
| dc.date.available | 2026-07-07T12:53:00Z | |
| dc.description | For a smooth and proper curve X over the fraction field K of a discrete valuation ring R, we explain (under very mild hypotheses) how to equip the de Rham cohomology H^1_{dR}(X/K) with a canonical integral structure: i.e. an R-lattice which is functorial in finite (generically etale) K-morphisms of X and which is preserved by the cup-product auto-duality on H^1_{dR}(X/K). Our construction of this lattice uses a certain class of normal proper models of X and relative dualizing sheaves. We show that our lattice naturally contains the lattice furnished by the (truncated) de Rham complex of a regular proper R-model of X and that the index for this inclusion of lattices is a numerical invariant of X (we call it the de Rham conductor). Using work of Bloch and Liu-Saito, we prove that the de Rham conductor of X is bounded above by the Artin conductor, and bounded below by the Efficient conductor. We then study how the position of our canonical lattice inside the de Rham cohomology of X is affected by finite extension of scalars. | |
| dc.description | 35 pages. See also http://www.math.mcgill.ca/bcais/index.html | |
| dc.identifier | https://arxiv.org/abs/0806.2688 | |
| dc.identifier | http://arxiv.org/abs/0806.2688 | |
| dc.identifier | Annales de l'Institut Fourier, Volume 59 (2009) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223480 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14F40 (Primary), 11G20, 14F30, 14G20, 14H25 (Secondary) | |
| dc.title | Canonical integral structures on the de Rham cohomology of curves | |
| dc.type | text |