The ABC theorem for higher-dimensional function fields

Liang-Chung Hsia, Julie Tzu Yueh Wang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We generalize the ABC theorems to the function field of a variety over an algebraically closed field of arbitrary characteristic which is non-singular in codimension one. We also obtain an upper bound for the minimal order sequence of Wronskians over such function fields of positive characteristic.

Original languageEnglish
Pages (from-to)2871-2887
Number of pages17
JournalTransactions of the American Mathematical Society
Volume356
Issue number7
DOIs
Publication statusPublished - 2004 Jul 1

Fingerprint

Function Fields
High-dimensional
Wronskian
Positive Characteristic
Algebraically closed
Theorem
Codimension
Upper bound
Generalise
Arbitrary

Keywords

  • ABC theorem
  • Diophantine approximation
  • Function fields

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The ABC theorem for higher-dimensional function fields. / Hsia, Liang-Chung; Wang, Julie Tzu Yueh.

In: Transactions of the American Mathematical Society, Vol. 356, No. 7, 01.07.2004, p. 2871-2887.

Research output: Contribution to journalArticle

@article{7770da08e7d943ff92ee5bc33e823daf,
title = "The ABC theorem for higher-dimensional function fields",
abstract = "We generalize the ABC theorems to the function field of a variety over an algebraically closed field of arbitrary characteristic which is non-singular in codimension one. We also obtain an upper bound for the minimal order sequence of Wronskians over such function fields of positive characteristic.",
keywords = "ABC theorem, Diophantine approximation, Function fields",
author = "Liang-Chung Hsia and Wang, {Julie Tzu Yueh}",
year = "2004",
month = "7",
day = "1",
doi = "10.1090/S0002-9947-03-03363-4",
language = "English",
volume = "356",
pages = "2871--2887",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "7",

}

TY - JOUR

T1 - The ABC theorem for higher-dimensional function fields

AU - Hsia, Liang-Chung

AU - Wang, Julie Tzu Yueh

PY - 2004/7/1

Y1 - 2004/7/1

N2 - We generalize the ABC theorems to the function field of a variety over an algebraically closed field of arbitrary characteristic which is non-singular in codimension one. We also obtain an upper bound for the minimal order sequence of Wronskians over such function fields of positive characteristic.

AB - We generalize the ABC theorems to the function field of a variety over an algebraically closed field of arbitrary characteristic which is non-singular in codimension one. We also obtain an upper bound for the minimal order sequence of Wronskians over such function fields of positive characteristic.

KW - ABC theorem

KW - Diophantine approximation

KW - Function fields

UR - http://www.scopus.com/inward/record.url?scp=2942659827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942659827&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-03-03363-4

DO - 10.1090/S0002-9947-03-03363-4

M3 - Article

VL - 356

SP - 2871

EP - 2887

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 7

ER -