Geodesic
Szpiro's small points conjecture for cyclic covers
Documenta mathematica, Tome 19 (2014), pp. 1085-1103.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $X$ be a smooth, projective and geometrically connected curve of genus at least two, defined over a number field. In 1984, Szpiro conjectured that $X$ has a «small point». In this paper we prove that if $X$ is a cyclic cover of prime degree of the projective line, then $X$ 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.
Classification : 14G05, 14G40, 11J86
Keywords: Szpiro's small points conjecture, cyclic covers, Arakelov theory, arithmetic surfaces, theory of logarithmic forms 
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     author = {Javanpeykar, Ariyan and von K\"anel, Rafael},
     title = {Szpiro's small points conjecture for cyclic covers},
     journal = {Documenta mathematica},
     pages = {1085--1103},
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     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a8/}
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Javanpeykar, Ariyan; von Känel, Rafael. Szpiro's small points conjecture for cyclic covers. Documenta mathematica, Tome 19 (2014), pp. 1085-1103. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a8/