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On Certain Uniformity Properties of Curves Over Function Fields

Published online by Cambridge University Press:  04 December 2007

Lucia Caporaso
Lucia Caporaso
Affiliation:
Department of Mathematics, Massachusetts Istitute of Technology, Cambridge, MA 02139, U.S.A.. E-mail: caporaso@math.mit.edu
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Abstract

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A uniform version of the Shafarevich Conjecture for function fields (Theorem of Parshin–Arakelov) is proved, together with a uniform version of the geometric Mordell conjecture (Theorem of Manin). Such results are generalized to base varieties of arbitrary dimension (i.e. function fields of arbitrary transcendence degree).

Keywords

function fieldcurverational point
Type
Research Article
Information
Compositio Mathematica , Volume 130 , Issue 1 , January 2002 , pp. 1 - 19
Copyright
© 2002 Kluwer Academic Publishers