Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture

Shushi Harashita[1]

  • [1] Yokohama National University Graduate School of Environment and Information Sciences 79-7 Tokiwadai, Hodogaya-ku Yokohama 240-8501(Japan)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 5, page 1787-1830
  • ISSN: 0373-0956

Abstract

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We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of p -kernel.

How to cite

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Harashita, Shushi. "Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture." Annales de l’institut Fourier 60.5 (2010): 1787-1830. <http://eudml.org/doc/116321>.

@article{Harashita2010,
abstract = {We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of $p$-kernel.},
affiliation = {Yokohama National University Graduate School of Environment and Information Sciences 79-7 Tokiwadai, Hodogaya-ku Yokohama 240-8501(Japan)},
author = {Harashita, Shushi},
journal = {Annales de l’institut Fourier},
keywords = {Abelian varieties; the Newton polygon stratification; the Ekedahl-Oort stratification; Oort’s conjecture; Oort's conjecture},
language = {eng},
number = {5},
pages = {1787-1830},
publisher = {Association des Annales de l’institut Fourier},
title = {Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture},
url = {http://eudml.org/doc/116321},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Harashita, Shushi
TI - Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 5
SP - 1787
EP - 1830
AB - We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of $p$-kernel.
LA - eng
KW - Abelian varieties; the Newton polygon stratification; the Ekedahl-Oort stratification; Oort’s conjecture; Oort's conjecture
UR - http://eudml.org/doc/116321
ER -

References

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