Algebraic jet spaces and Zilber’s dichotomy in DCFA
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| Údar: | |
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| Formáid: | artículo original |
| Stádas: | Versión publicada |
| Fecha de Publicación: | 2010 |
| Cur Síos: | This is the first of two papers devoted to the proof of Zilber’s dichotomy for the case of difference-differential fields of characteristic zero. In this paper we use the techniques exposed in [9] to prove a weaker version of the dichotomy, more precisely, we prove the following: in DCFA the canonical base of a finite-dimensional type is internal to the fixed field of the field of constants. This will imply a weak version of Zilber’s dichotomy: a finite-dimensional type of SU -rank 1 is either 1-based or non-orthogonal to the fixed field of the field of constants. |
| País: | Portal de Revistas UCR |
| Institiúid: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Teanga: | Español |
| OAI Identifier: | oai:archivo.portal.ucr.ac.cr:article/308 |
| Rochtain Ar Líne: | https://archivo.revistas.ucr.ac.cr/index.php/matematica/article/view/308 |
| Palabra clave: | Model Theory of Fields Supersimple Theories Difference-Differential Fields Definable Sets Teoría de modelos teorías supersimples campos diferenciales de diferencia conjuntos definibles |