TY - JOUR
T1 - A variety that cannot be dominated by one that lifts
AU - van Dobben De Bruyn, Remy
N1 - Publisher Copyright:
© 2020
PY - 2021/4/1
Y1 - 2021/4/1
N2 - We prove a strong version of a theorem of Siu and Beauville on morphisms to higher genus curves, and we use it to show that if a variety X in characteristic p lifts to characteristic 0, then any morphism X ! C to a curve of genus g ≥ 2 can be lifted along. We use this to construct, for every prime p, a smooth projective surface X over FNp that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.
AB - We prove a strong version of a theorem of Siu and Beauville on morphisms to higher genus curves, and we use it to show that if a variety X in characteristic p lifts to characteristic 0, then any morphism X ! C to a curve of genus g ≥ 2 can be lifted along. We use this to construct, for every prime p, a smooth projective surface X over FNp that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.
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U2 - 10.1215/00127094-2020-0055
DO - 10.1215/00127094-2020-0055
M3 - Review article
AN - SCOPUS:85105064777
SN - 0012-7094
VL - 1
SP - 1
EP - 39
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -