Systems of cubic forms

• Autores: Rainer Dietmann
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 666-686
• Idioma: inglés
• DOI: 10.1112/jlms/jdm123
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• Resumen

  • We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we prove that for p2 any system of r cubic forms over Qp in more than 125r3+705r2+210r variables admits a non-trivial p-adic zero, and that any system of r rational cubic forms in more than O(r4 m6+r6 m5) variables admits a rational linear space of zeros of dimension at least m.