Elliptic curves over function fields with a large set of integral points

Ricardo Concei\c{c}\~ao

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Elliptic curves over function fields with a large set of integral points

Ricardo Conceição

Number Theory · Submitted 18 Oct 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We construct isotrivial and non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ with an arbitrarily large set of separable integral points.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.42 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We construct isotrivial and non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over $\mathbb_{F}_q(t)$ with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily large set of linearly independent points.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct isotrivial and non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ with an arbitrarily large set of separable integral points.	contribution 0.66	0.97	0.77	asserted 1.00
s1	As an application of this construction, we prove that there are isotrivial log-general type varieties over $\mathbb_{F}_q(t)$ with a Zariski dense set of separable integral points.	result 0.88	0.95	0.23	asserted 1.00
s2	This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting.	interpretation 0.99	0.84	0.50	asserted 1.00
s3	We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily large set of linearly independent points.	result 0.91	0.95	0.17	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We construct isotrivial and non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over $\mathbb_{F}_q(t)$ with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily large set of linearly independent points.

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Builds on it 1 paper

In this paper we provide counterexamples to this uniform boundedness, extending constructions of the first two authors [ref] for elliptic curves.

Unboundedness of the number of rational points on curves over function fields · Introduction · 1.00

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