Generalization of Deuring Reduction Theorem

@article{Zaytsev2012GeneralizationOD,
  title={Generalization of Deuring Reduction Theorem},
  author={A. Zaytsev},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
  • A. Zaytsev
  • Published 2012
  • Mathematics
  • arXiv: Algebraic Geometry
In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM field $K$ over a number field at a pace of good reduction. We establish a connection between a decomposition of the first truncated Barsotti-Tate group scheme $A[p]$ and a decomposition of $p\cO_{K}$ into prime ideals. In particular, we produce these explicit… Expand
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References

SHOWING 1-10 OF 18 REFERENCES
ABELIAN VARIETIES OVER FINITE FIELDS.
  • S. Lang
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1955
Group schemes with additional structures and Weyl group cosets
The structure of Galois groups of -fields
THE STRUCTURE OF GALOIS GROUPS OF CM-FIELDS
Lectures on Hilbert Modular Varieties and Modular Forms
Simple p-kernels of p-divisible groups
Lectures on p-divisible groups
The first de Rham cohomology group and Dieudonné modules
Complex Multiplication
  • G. Frey, T. Lange
  • Computer Science
  • Handbook of Elliptic and Hyperelliptic Curve Cryptography
  • 2005
...
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2
...