대한수학회지 (Journal of the Korean Mathematical Society)

  • 제61권3호
  • /
  • Pages.515-545
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  • 2024
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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REDUCTION OF ABELIAN VARIETIES AND CURVES

  • 투고 : 2023.07.15
  • 심사 : 2023.11.11
  • 발행 : 2024.05.01
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초록

Consider a Noetherian domain R0 with quotient field K0. Let K be a finitely generated regular transcendental field extension of K0. We construct a Noetherian domain R with Quot(R) = K that contains R0 and embed Spec(R0) into Spec(R). Then, we prove that key properties of abelian varieties and smooth geometrically integral projective curves over K are preserved under reduction modulo p for "almost all" p ∈ Spec(R0).

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참고문헌

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