Explicit construction of a global uniformization for an algebraic correspondence

Quantitative Riemann existence theorem over a number field

“…It would be interesting to re-consider his work and try to justify his argument. This would not only improve on the estimates of this article, but would also probably imply a relatively practical algorithm (see [6] for some indications) for actual calculation of the polynomial f . Evidently, our equations are too bulky for this purpose.…”

“…Proof of Proposition 2. 6 We denote by V the algebraic set defined by (2.2). Since it has a 0-dimensional component α, we have k ≥ N. Among the k polynomials p 1 , .…”