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

Voir la notice de l'article dans 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},
     journal = {Documenta mathematica},
     pages = {957--972},
     publisher = {mathdoc},
     volume = {15},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a5/}
}
TY  - JOUR
AU  - Starr, Jason
AU  - De Jong, Johan
TI  - Almost proper GIT-stacks and discriminant avoidance
JO  - Documenta mathematica
PY  - 2010
SP  - 957
EP  - 972
VL  - 15
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a5/
LA  - en
ID  - DOCMA_2010__15__a5
ER  - 
%0 Journal Article
%A Starr, Jason
%A De Jong, Johan
%T Almost proper GIT-stacks and discriminant avoidance
%J Documenta mathematica
%D 2010
%P 957-972
%V 15
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a5/
%G en
%F DOCMA_2010__15__a5
Starr, Jason; De Jong, Johan. Almost proper GIT-stacks and discriminant avoidance. Documenta mathematica, Tome 15 (2010), pp. 957-972. https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a5/