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Vol. 15 Núm. 1 (2024)
Vol 15, Núm.1 (2024): Enero-Junio

Revisiones/Reviews

Una revisión a las geometrías de Zariski uno–dimensionales

https://doi.org/10.19053/01217488.v15.n1.2024.16237

Publicado 2024-02-12

  • Joel Torres del Valle
    • ,
  • Pedro Rizzo

Joel Torres del Valle
a:1:{s:5:"es_ES";s:24:"Universidad de Antioquia";}

Pedro Rizzo
Universidad de Antioquia

Resumen

En este artıculo, realizamos una revisión de las geometrías de Zariski de dimensión uno. Comenzamos con una breve retrospectiva de conceptos clave en toria de modelos y su evolución histórica. Luego, introducimos conceptos en geometría algebraica, explorando la intersección con la teoría  de modelos para motivar la teoría de modelos geométrica. Destacamos la Conjetura de tricotomía de Zilber y como la refutación  de Hrushovski condujo a Zilber y Hrushovski a aislar la clase de estructuras donde la conjetura tiene validez, dando origen a las geometrías de Zariski. Concluimos presentando los resultados

obtenidos por Zilber y Hrushovski en los 90s y ofrecemos una revision bibliográfica  actualizada del tema.

PDF

Citas

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