Slope-determinant method, complex cellular structures and hypersurface coverings of regular rational points
arXiv:2412.05205
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.
13 pages, comments welcome!