Geodesic
Almost proper GIT-stacks and discriminant avoidance
Documenta mathematica, Tome 15 (2010), pp. 957-972.

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

Summary: We prove that the classifying stack of an reductive group scheme over a field is very close to being proper. Using this we prove a result about isotrivial families of varieties. Fix a polarized variety with reductive automorphism group. To prove that every isotrivial family with this fibre has a rational section it suffices to prove this when the base is projective, i.e., the discriminant of the family is empty. 
@article{DOCMA_2010__15__a5,
     author = {Starr, Jason and De Jong, Johan},
     title = {Almost proper {GIT-stacks} and discriminant avoidance},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2010__15__a5/}
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Starr, Jason; De Jong, Johan. Almost proper GIT-stacks and discriminant avoidance. Documenta mathematica, Tome 15 (2010), pp. 957-972. http://geodesic.mathdoc.fr/item/DOCMA_2010__15__a5/