Title: Bounds for multivariate residues and for the polynomials in the elimination theorem,
Abstract: We present several upper bounds for the height of global residues of rational
forms on an affine variety. As a consequence, 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. This is an arithmetic analogue
of Jelonek's effective elimination theorem, that plays a crucial role in the
proof of our bounds for the height of global residues.