Abelian varieties over cyclic fields

• Autores: Boe-Hae Im, Michael D. Larsen
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 5, 2008, págs. 1195-1210
• Idioma: inglés
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• Resumen

  • Let $K$ be a field of characteristic $\neq 2$ such that every finite separable extension of $K$ is cyclic. Let $A$ be an abelian variety over $K$. If $K$ is infinite, then $A(K)$ is Zariski-dense in $A$. If $K$ is not locally finite, the rank of $A$ over $K$ is infinite.