Resumen de Systems of cubic forms

Rainer Dietmann

• 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.