On the global determinant method

Abstract

In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also explain why some constants will be more explicit if we admit the Generalized Riemann Hypothesis.

39 pages. arXiv admin note: text overlap with arXiv:1910.00306

References in corpus (1)

• Control of the non-geometrically integral reductions

Cited by in corpus (1)

• Uniform bounds for the number of rational points on varieties over global fields