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

Published online by Cambridge University Press:  14 May 2019

Nobuo Tsuzuki*
Affiliation:
Mathematical Institute, Tohoku University, Aza-Aoba 6-3, Aramaki, Aobaku, Sendai, 980-8578, Japan ([email protected])

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.

Type
Research Article
Copyright
© Cambridge University Press 2019

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