Bounds for Multivariate Residues and for the Polynomials in the Elimination Theorem
Martı́n Sombra, Alain Yger · Moscow Mathematical Journal · 2021
We present several upper bounds for the height of global residues of rational forms on an affine variety defined over Q.As an application, we deduce upper bounds for the height of the coefficients in the Bergman-Weil trace formula.We also present upper bounds for the degree and the height of the polynomials in the elimination theorem on an affine variety defined over Q.This is an arithmetic analogue of Jelonek's effective elimination theorem, and it plays a crucial role in the proof of our bounds for the height of global residues.Contents 1. Introduction 1 2. Global residues on affine varieties 5 3. Residues on the affine line 15 4. Residues on an affine variety: polynomials in separated variables 20 5.An arithmetic elimination theorem 26 6.Residues on an affine variety: the general case 33 References 40