Algebraic jet spaces and Zilber’s dichotomy in DCFA | Zendy

Ronald F. Bustamante Medina | Zendy

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Algebraic jet spaces and Zilber’s dichotomy in DCFA

Author(s) -

Ronald F. Bustamante Medina

Publication year - 2010

Publication title -

revista de matemática teoría y aplicaciones

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.

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