Open AccessAlgebraic jet spaces and Zilber’s dichotomy in DCFA
Author(s) -
Ronald F. Bustamante Medina
Publication year - 2010
Publication title -
revista de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2215-3373
pISSN - 1409-2433
DOI - 10.15517/rmta.v17i1.308
Subject(s) - mathematics , pure mathematics , algebraic number , rank (graph theory) , field (mathematics) , type (biology) , differential (mechanical device) , differential algebra , algebra over a field , combinatorics , mathematical analysis , physics , ecology , biology , thermodynamics
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.