Weak approximation on del Pezzo surfaces of degree 1

• Autores: Anthony Várilly Alvarado
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 6, 2008, págs. 2123-2145
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.08.007
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• Resumen

  • We study del Pezzo surfaces of degree 1 of the form w2=z3+Ax6+By6in the weighted projective space , where k is a perfect field of characteristic not 2 or 3 and A,Bk*. Over a number field, we exhibit an infinite family of (minimal) counterexamples to weak approximation amongst these surfaces, via a Brauer�Manin obstruction.