TY - JOUR
T1 - CONSTANCY of NEWTON POLYGONS OF-ISOCRYSTALS on ABELIAN VARIETIES and ISOTRIVIALITY of FAMILIES of CURVES
AU - Tsuzuki, Nobuo
N1 - Funding Information:
Acknowledgments. The author thanks Professor Takao Yamazaki and Professor Jeng-Daw Yu for useful discussions. The author also thanks Professor Yifan Yang who told the author important examples of Shimura curves. The examples inspired the author to study the constancy problem of Newton polygons. The author thanks the anonymous referee for his/her useful comments. The author is supported by Grant-in-Aid for Exploratory Research (15K13422) and Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers (R2701), Japan Society for the Promotion of Science.
Publisher Copyright:
© 2019 Cambridge University Press.
PY - 2021/3
Y1 - 2021/3
N2 - We prove constancy of Newton polygons of all convergent-isocrystals on Abelian varieties over finite fields. Applying the constancy, we prove the isotriviality of proper smooth families of curves over Abelian varieties. More generally, we prove the isotriviality over projective smooth varieties on which any convergent-isocrystal has constant Newton polygons.
AB - We prove constancy of Newton polygons of all convergent-isocrystals on Abelian varieties over finite fields. Applying the constancy, we prove the isotriviality of proper smooth families of curves over Abelian varieties. More generally, we prove the isotriviality over projective smooth varieties on which any convergent-isocrystal has constant Newton polygons.
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U2 - 10.1017/S1474748019000276
DO - 10.1017/S1474748019000276
M3 - Article
AN - SCOPUS:85065635928
SN - 1474-7480
VL - 20
SP - 587
EP - 625
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
IS - 2
ER -