Prolongations in differential algebra
| dc.creator | Rosen, Eric | |
| dc.date | 2005-10-11 | |
| dc.date | 2007-09-18 | |
| dc.date.accessioned | 2026-07-07T08:30:10Z | |
| dc.date.available | 2026-07-07T08:30:10Z | |
| dc.description | We develop the theory of higher prolongations of algebraic varieties over fields in arbitrary characteristic with commuting Hasse-Schmidt derivations. Prolongations were introduced by Buium in the context of fields of characteristic 0 with a single derivation. Inspired by work of Vojta, we give a new construction of higher prolongations in a more general context. Generalizing a result of Buium in characteristic 0, we prove that these prolongations are represented by a certain functor, which shows that they can be viewed as `twisted jet spaces.' We give a new proof of a theorem of Moosa, Pillay, and Scanlon that the prolongation functor and jet space functor commute. We also prove that the $m^{th}$-prolongation and $m^{th}$-jet space of a variety are differentially isomorphic by showing that their infinite prolongations are isomorphic as schemes. | |
| dc.description | Expanded introduction and minor revisions, 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0510235 | |
| dc.identifier | http://arxiv.org/abs/math/0510235 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138175 | |
| dc.subject | Logic | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 12H05 | |
| dc.title | Prolongations in differential algebra | |
| dc.type | text |