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Purity of the stratification by Newton polygons

Author(s): A. J. de Jong; F. Oort
Journal: J. Amer. Math. Soc. 13 (2000), 209-241.
MSC (2000): Primary 14L05, 14B05
Posted: September 22, 1999
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Abstract: Let $S$ be a variety in characteristic $p>0$. Suppose we are given a nondegenerate $F$-crystal over $S$, for example the $i$th relative crystalline cohomology sheaf of a family of smooth projective varieties over $S$. At each point $s$ of $S$ we have the Newton polygon associated to the action of $F$ on the fibre of the crystal at $s$. According to a theorem of Grothendieck the Newton polygon jumps up under specialization. The main theorem of this paper is that the jumps occur in codimension $1$ on $S$ (the Purity Theorem). As an application we prove some results on deformations of iso-simple $p$-divisible groups.

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Additional Information:

A. J. de Jong
Affiliation: Massachusetts Institute of Technology, Department of Mathematics, Building 2, Room 270, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: dejong@math.mit.edu

F. Oort
Affiliation: Universiteit Utrecht, Mathematisch Instituut, Budapestlaan 6, NL-3508 TA Utrecht, The Netherlands
Email: oort@math.uu.nl

DOI: 10.1090/S0894-0347-99-00322-7
PII: S 0894-0347(99)00322-7
Received by editor(s): October 28, 1998
Received by editor(s) in revised form: July 27, 1999
Posted: September 22, 1999
Additional Notes: The research of Dr. A.J. de Jong has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.
Copyright of article: Copyright 1999, American Mathematical Society

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