Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MORPHISMS OF VARIETIES OVER AMPLE FIELDS

  • Received : 2017.06.01
  • Accepted : 2018.02.27
  • Published : 2018.07.31
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Abstract

We strengthen a result of Michiel Kosters by proving the following theorems: (*) Let ${\phi}:W{\rightarrow}V$ be a finite surjective morphism of algebraic varieties over an ample field K. Suppose V has a simple K-rational point a such that $a{\not\in}{\phi}(W(K_{ins}))$. Then, card($V(K){\backslash}{\phi}(W(K))$ = card(K). (**) Let K be an infinite field of positive characteristic and let $f{\in}K[X]$ be a non-constant monic polynomial. Suppose all zeros of f in $\tilde{K}$ belong to $K_{ins}{\backslash}K$. Then, card(K \ f(K)) = card(K).

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