### Abstract

The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic p > 2. The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.

Original language | English (US) |
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Pages (from-to) | 493-498 |

Number of pages | 6 |

Journal | Mathematical Notes of the Academy of Sciences of the USSR |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 1977 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*Mathematical Notes of the Academy of Sciences of the USSR*, vol. 22, no. 1, pp. 493-498. https://doi.org/10.1007/BF01147687

**Torsion of Abelian varieties of finite characteristic.** / Zarkhin, Yuriy G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Torsion of Abelian varieties of finite characteristic

AU - Zarkhin, Yuriy G.

PY - 1977/7/1

Y1 - 1977/7/1

N2 - The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic p > 2. The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.

AB - The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic p > 2. The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.

UR - http://www.scopus.com/inward/record.url?scp=34250284051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250284051&partnerID=8YFLogxK

U2 - 10.1007/BF01147687

DO - 10.1007/BF01147687

M3 - Article

AN - SCOPUS:34250284051

VL - 22

SP - 493

EP - 498

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1

ER -