Morphisms of varieties over ample fields

Lior Bary-Soroker; Wulf Dieter Geyer; Moshe Jarden

doi:10.4134/BKMS.b170483

Morphisms of varieties over ample fields

Lior Bary-Soroker
, Wulf Dieter Geyer
, Moshe Jarden

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-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 (K_ins)). 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 K_ins \ K. Then, card(K \ f(K)) = card(K).

Original language	English
Pages (from-to)	1023-1035
Number of pages	13
Journal	Bulletin of the Korean Mathematical Society
Volume	55
Issue number	4
DOIs	https://doi.org/10.4134/BKMS.b170483
State	Published - 2018

Keywords

Ample fields
Morphisms of varieties

ASJC Scopus subject areas

General Mathematics

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10.4134/BKMS.b170483

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title = "Morphisms of varieties over ample fields",

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) \textbackslash{} 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 \textbackslash{} K. Then, card(K \textbackslash{} f(K)) = card(K).",

keywords = "Ample fields, Morphisms of varieties",

author = "Lior Bary-Soroker and Geyer, \{Wulf Dieter\} and Moshe Jarden",

note = "Publisher Copyright: {\textcopyright}2018 Korean Mathematial Soiety.",

year = "2018",

doi = "10.4134/BKMS.b170483",

language = "الإنجليزيّة",

volume = "55",

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journal = "Bulletin of the Korean Mathematical Society",

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TY - JOUR

T1 - Morphisms of varieties over ample fields

AU - Bary-Soroker, Lior

AU - Geyer, Wulf Dieter

AU - Jarden, Moshe

PY - 2018

Y1 - 2018

N2 - 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).

AB - 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).

KW - Ample fields

KW - Morphisms of varieties

UR - https://www.scopus.com/pages/publications/85051678893

U2 - 10.4134/BKMS.b170483

DO - 10.4134/BKMS.b170483

M3 - مقالة

SN - 1015-8634

VL - 55

SP - 1023

EP - 1035

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 4

ER -

Morphisms of varieties over ample fields

Abstract

Keywords

ASJC Scopus subject areas

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