Morphisms of varieties over ample fields

Lior Bary-Soroker, Wulf Dieter Geyer, Moshe Jarden

Research output: Contribution to journalArticlepeer-review

Abstract

We strengthen a result of Michiel Kosters by proving the following theorems: (∗) Let φ: W → 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 ∉ φ(W (Kins)). Then, card(V (K) \ φ(W (K)) = card(K). (∗∗) Let K be an infinite field of positive characteristic and let f ∈ K[X] be a non-constant monic polynomial. Suppose all zeros of f in K belong to Kins \ K. Then, card(K \ f(K)) = card(K).

Original languageEnglish
Pages (from-to)1023-1035
Number of pages13
JournalBulletin of the Korean Mathematical Society
Volume55
Issue number4
DOIs
StatePublished - 2018

Keywords

  • Ample fields
  • Morphisms of varieties

All Science Journal Classification (ASJC) codes

  • General Mathematics

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