A Simple Remark on Fields of Definition

• Hidalgo, Ruben A. ^[1]
  1. [1] Universidad Técnica Federico Santa María.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 1, 2012, págs. 25-28
• Idioma: inglés
• DOI: 10.4067/S0716-09172012000100003
• Enlaces
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• Resumen

  • Let K< L be an extension of fields, in characteristic zero, with L algebraically closed and let ‾K;< L be the algebraic closure of K in L. Let X and Y be irreducible projective algebraic varieties, X defined over ‾K and Y defined over L, and let π : X → Y be a non-constant morphism, defined over L. If we assume that ‾K ≠ L,then one may wonder if Y is definable over ‾K. In the case that K = Q, L = C and that X and Y are smooth curves, a positive answer was obtained by Gonzalez-Diez. In this short note we provide simple conditions to have a positive answer to the above question. We also state a conjecture for a class of varieties of general type. 

• Referencias bibliográficas
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  • [3] H. Hammer and F Herrlich. A Remark on the Moduli Field of a Curve. Arch. Math. 81 (2003), 5-10.
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