Ekedahl-Oort strata and the first Newton slope strata
Author:
Shushi Harashita
Journal:
J. Algebraic Geom. 16 (2007), 171-199
DOI:
https://doi.org/10.1090/S1056-3911-06-00451-6
Published electronically:
September 26, 2006
MathSciNet review:
2257323
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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
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- F. Oort, Commutative group schemes, Lecture Notes in Mathematics, vol. 15, Springer-Verlag, Berlin-New York, 1966. MR 0213365
- Frans Oort, A stratification of a moduli space of abelian varieties, Moduli of abelian varieties (Texel Island, 1999) Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 345–416. MR 1827027, DOI https://doi.org/10.1007/978-3-0348-8303-0_13
- Frans Oort, Foliations in moduli spaces of abelian varieties, J. Amer. Math. Soc. 17 (2004), no. 2, 267–296. MR 2051612, DOI https://doi.org/10.1090/S0894-0347-04-00449-7
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References
- M. Demazure: Lectures on $p$-divisible groups. Lecture Notes in Mathematics, 302, Springer-Verlag, Berlin-New York, 1972. MR 0344261 (49:9000)
- T. Ekedahl and G. van der Geer: Cycle classes of the E-O stratification on the moduli of abelian varieties. Preprint: math.AG/0412272.
- E. Z. Goren and F. Oort: Stratifications of Hilbert Modular Varieties. J. Algebraic Geom. 9 (2000), no. 1, 111–154. MR 1713522 (2000g:14034)
- 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)
- 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)
- F. Oort: Commutative group schemes. Lecture Notes in Mathematics, 15, Springer-Verlag, Berlin-New York, 1966. MR 0213365 (35:4229)
- 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)
- F. Oort: Foliations in moduli spaces of abelian varieties. J. Amer. Math. Soc. 17 (2004), no. 2, 267–296. MR 2051612 (2005c:14051)
- 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)
- 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
Received by editor(s):
August 22, 2005
Received by editor(s) in revised form:
January 12, 2006, and February 20, 2006
Published electronically:
September 26, 2006