Unboundedness of the number of rational points on curves over function fields

Ricardo Conceição; Douglas Ulmer; José Felipe Voloch

Unboundedness of the number of rational points on curves over function fields

Ricardo Conceição
, Douglas Ulmer
, José Felipe Voloch

Research output: Contribution to journal › Article › peer-review

Abstract

We construct sequences of smooth nonisotrivial curves of every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence cannot be uniformly bounded.

Original language	English (US)
Pages (from-to)	291-293
Number of pages	3
Journal	New York Journal of Mathematics
Volume	18
State	Published - Apr 26 2012
Externally published	Yes

Keywords

Algebraic curves
Function fields
Rational points

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Unboundedness of the number of rational points on curves over function fields",

abstract = "We construct sequences of smooth nonisotrivial curves of every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence cannot be uniformly bounded.",

keywords = "Algebraic curves, Function fields, Rational points",

author = "Ricardo Concei{\c c}{\~a}o and Douglas Ulmer and Voloch, \{Jos{\'e} Felipe\}",

year = "2012",

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day = "26",

language = "English (US)",

volume = "18",

pages = "291--293",

journal = "New York Journal of Mathematics",

issn = "1076-9803",

publisher = "University at Albany",

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T1 - Unboundedness of the number of rational points on curves over function fields

AU - Conceição, Ricardo

AU - Ulmer, Douglas

AU - Voloch, José Felipe

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N2 - We construct sequences of smooth nonisotrivial curves of every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence cannot be uniformly bounded.

AB - We construct sequences of smooth nonisotrivial curves of every genus at least two, defined over a rational function field of positive characteristic, such that the (finite) number of rational points of the curves in the sequence cannot be uniformly bounded.

KW - Algebraic curves

KW - Function fields

KW - Rational points

UR - https://www.scopus.com/pages/publications/84875463282

UR - https://www.scopus.com/pages/publications/84875463282#tab=citedBy

M3 - Article

AN - SCOPUS:84875463282

SN - 1076-9803

VL - 18

SP - 291

EP - 293

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Unboundedness of the number of rational points on curves over function fields

Abstract

Keywords

ASJC Scopus subject areas

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