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CONSTANCY OF NEWTON POLYGONS OF $F$-ISOCRYSTALS ON ABELIAN VARIETIES AND ISOTRIVIALITY OF FAMILIES OF CURVES

Part of: Curves (Co)homology theory

Published online by Cambridge University Press:  14 May 2019

Nobuo Tsuzuki
Nobuo Tsuzuki*
Affiliation:
Mathematical Institute, Tohoku University, Aza-Aoba 6-3, Aramaki, Aobaku, Sendai, 980-8578, Japan (tsuzuki@math.tohoku.ac.jp)
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Abstract

We prove constancy of Newton polygons of all convergent $F$-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 $F$-isocrystal has constant Newton polygons.

Keywords

F-isocrystalNewton polygonisotriviality of families of curves

MSC classification

Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14H10: Families, moduli (algebraic)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 2 , March 2021 , pp. 587 - 625
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Copyright
© Cambridge University Press 2019

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