Quantitative Néron theory for torsion bundles
| dc.creator | Chiodo, Alessandro | |
| dc.date | 2006-03-29 | |
| dc.date | 2007-04-02 | |
| dc.date.accessioned | 2026-07-07T07:54:56Z | |
| dc.date.available | 2026-07-07T07:54:56Z | |
| dc.description | Let R be a discrete valuation ring with algebraically closed residue field, and consider a smooth curve CK over the field of fractions K. For any positive integer r prime to the residual characteristic, we consider the finite K-group scheme Pic_{CK}[r] of r-torsion line bundles on CK. We determine when there exists a finite R-group scheme, which is a model of Pic_{CK}[r] over R; in other words, we establish when the Néron model of Pic_{CK}[r] is finite. To this effect, one needs to analyse the points of the Néron model over R, which, in general, do not represent r-torsion line bundles on a semistable reduction of CK. Instead, we recast the notion of models on a stack-theoretic base: there, we find finite Néron models, which represent r-torsion line bundles on a stack-theoretic semistable reduction of CK. This allows us to quantify the lack of finiteness of the classical Néron models and finally to provide an efficient criterion for it. | |
| dc.description | 26 pages, v2 exposition improved, introduction rewritten, a new application (Cor. 5.5.1) and a new section (\S7) added; | |
| dc.identifier | https://arxiv.org/abs/math/0603689 | |
| dc.identifier | http://arxiv.org/abs/math/0603689 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126802 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Quantitative Néron theory for torsion bundles | |
| dc.type | text |