Algebraic jet spaces and Zilber’s dichotomy in DCFA
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 canon...
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Format: | Article |
Language: | English |
Published: |
Universidad de Costa Rica
2010-04-01
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Series: | Revista de Matemática: Teoría y Aplicaciones |
Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/308 |
Summary: | 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. |
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ISSN: | 2215-3373 |