Journal of Algebraic Geometry Journal of Algebraic Geometry

     

Ekedahl-Oort strata and the first Newton slope strata

Author(s): Shushi Harashita
Journal: J. Algebraic Geom. 16 (2007), 171-199.
Posted: September 26, 2006
Retrieve article in: PDF DVI PostScript

Abstract | References | Additional information

Abstract: We investigate stratifications on the moduli space $ \mathcal{A}_g$ of principally polarized abelian varieties of dimension $ g$ in characteristic $ p>0$. In this paper we give an easy algorithm determining the first Newton slope of any generic point of each Ekedahl-Oort stratum.


References:

1.
M. Demazure: Lectures on $ p$-divisible groups. Lecture Notes in Mathematics, 302, Springer-Verlag, Berlin-New York, 1972. MR 0344261 (49:9000)

2.
T. Ekedahl and G. van der Geer: Cycle classes of the E-O stratification on the moduli of abelian varieties. Preprint: math.AG/0412272.

3.
E. Z. Goren and F. Oort: Stratifications of Hilbert Modular Varieties. J. Algebraic Geom. 9 (2000), no.1, 111-154. MR 1713522 (2000g:14034)

4.
N. M. Katz: Slope filtration of $ F$-crystals. Journ. Géom. Alg. Rennes, Vol. I, Astérisque 63 (1979), Soc. Math. France, 113-163. MR 0563463 (81i:14014)

5.
Yu. I. Manin, Theory of commutative formal groups over fields of finite characteristic. Uspehi Mat. Nauk 18 (1963) no.6 (114), 3-90; Russ. Math. Surveys 18 (1963), 1-80. MR 0157972 (28:1200)

6.
F. Oort: Commutative group schemes. Lecture Notes in Mathematics, 15, Springer-Verlag, Berlin-New York, 1966. MR 0213365 (35:4229)

7.
F. Oort: A stratification of a moduli space of abelian varieties. In: Moduli of abelian varieties (Ed. C. Faber, G. van der Geer, F. Oort), Progr. Math., 195, Birkhäuser, Basel, 2001; pp. 345-416. MR 1827027 (2002b:14055)

8.
F. Oort: Foliations in moduli spaces of abelian varieties. J. Amer. Math. Soc. 17 (2004), no.2, 267-296. MR 2051612 (2005c:14051)

9.
F. Oort: Newton Polygon Strata in the Moduli Space of Abelian Varieties. In: Moduli of abelian varieties (Ed. C. Faber, G. van der Geer, F. Oort), Progr. Math., 195, Birkhäuser, Basel, 2001; pp. 417-440. MR 1827028 (2002c:14069)

10.
F. Oort: Minimal $ p$-divisible groups. Ann. of Math. (2) 161 (2005), no.2, 1021-1036. MR 2153405


Additional Information:

Shushi Harashita
Affiliation: Department of Mathematics, Hokkaido University Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
Email: harasita@math.sci.hokudai.ac.jp

PII: S 1056-3911(06)00451-6
Received by editor(s): August 22, 2005
Received by editor(s) in revised form: January 12, 2006 and February 20, 2006
Posted: September 26, 2006

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2007 University Press, Inc.
Comments: jag-query@ams.org
AMS Website