Szpiro's small points conjecture for cyclic covers
Ariyan Javanpeykar
Rafael von Känel

Abstract
Let be a smooth, projective and geometrically connected curve of genus at least two, defined over a number field. In 1984, Szpiro conjectured that has a «small point». In this paper we prove that if is a cyclic cover of prime degree of the projective line, then has infinitely many «small points». In particular, we establish the first cases of Szpiro's small points conjecture, including the genus two case and the hyperelliptic case. The proofs use Arakelov theory for arithmetic surfaces and the theory of logarithmic forms.
Cite this article
Ariyan Javanpeykar, Rafael von Känel, Szpiro's small points conjecture for cyclic covers. Doc. Math. 19 (2014), pp. 1085–1103
DOI 10.4171/DM/475