Espacios de jets algebraicos y la dicotomía de Zilber en DCFA

• Bustamante Medina, Ronald F. ^[1]
  1. [1] Universidad de Costa Rica

     Universidad de Costa Rica

     Hospital, Costa Rica

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 17, Nº. 1, 2010, págs. 1-12
• Idioma: inglés
• DOI: 10.15517/rmta.v17i1.308
• Títulos paralelos:
  • Algebraic jet spaces and Zilber’s dichotomy in DCFA
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El presente es el primero de dos art´?culos dedicados a la demostraci´on de la dicotom´?a de Zilber para el caso de los camposdifernciales de diferencia de caracter´?stica cero. En ´este art´?culo utilizamoslas t´ecnicas desarrolladas en [9] para demostrar una versi´ond´ebil de la dicotom´?a: un tipo de dimensi´on finita y de rango SUigual a 1 es modular o no ortogonal al campo fijo del campo deconstantes.

  • English

    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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