Korean Journal of Mathematics

  • 제30권3호
  • /
  • Pages.555-560
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  • 2022
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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RESTRICTION OF SCALARS WITH SIMPLE ENDOMORPHISM ALGEBRA

  • Yu, Hoseog (Department of Mathematics and Statistics, Sejong University)
  • 투고 : 2022.02.18
  • 심사 : 2022.09.19
  • 발행 : 2022.09.30
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초록

Suppose L/K be a finite abelian extension of number fields of odd degree and suppose an abelian variety A defined over L is a K-variety. If the endomorphism algebra of A/L is a field F, the followings are equivalent : (1) The enodomorphiam algebra of the restriction of scalars from L to K is simple. (2) There is no proper subfield of L containing LGF on which A has a K-variety descent.

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참고문헌

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  4. A. Weil, Adeles and algebraic groups, Progr. Math. 23 (1982).
  5. H. Yu, Idempotent relations and the conjecture of Birch and Swinnerton-Dyer, Math. Ann. 327 (2003) 67-78. https://doi.org/10.1007/s00208-003-0427-8