Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REDUCTION OF ABELIAN VARIETIES AND CURVES

  • Received : 2023.07.15
  • Accepted : 2023.11.11
  • Published : 2024.05.01
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Abstract

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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References

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