Computing Weil's descente variety
We present sharp estimates for the degree and the height of the polynomials in the Nullstellensatz over ZZ. This result improves previous work of Berenstein-Yger and Krick-Pardo. We also present degree and height estimates of intrinsic type, which depend mainly on the degree and the height of the input polynomial system. As an application, we derive an effective arithmetic Nullstellensatz for sparse polynomial systems.