Remarks on S. Lang's conjecture over function fields

Atsushi Moriwaki

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arXiv · alg-geom/9412021

Remarks on S. Lang's conjecture over function fields

Atsushi Moriwaki

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Abstract

In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic zero, whose generic fiber is geometrically irreducible and of general type. If f is not birationally trivial, then there are countably many proper closed varieties { Z_i } of X such that every quasi-section of f is contained in the union of Z_i.

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Atsushi Moriwaki. 1994-12-24. Remarks on S. Lang's conjecture over function fields. https://arxiv.org/abs/alg-geom/9412021

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