Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points
Number Theory
2024-12-09 v1 Algebraic Geometry
Abstract
We use the determinant method of Bombieri-Pila and Heath-Brown and its Arakelov reformulation by Chen utilizing Bost's slope method to estimate the number of hypersurfaces required to cover the regular rational points with bounded Arakelov height on a projective variety. Using complex cellular structures introduced by Binyamini-Novikov, we replace the usual subpolynomial factor by a polylogarithmic factor in the estimation.
Cite
@article{arxiv.2412.05205,
title = {Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points},
author = {Kenneth Chung Tak Chiu},
journal= {arXiv preprint arXiv:2412.05205},
year = {2024}
}
Comments
13 pages, comments welcome!