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Towards the full Mordell-Lang conjecture for Drinfeld modules

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Dragos Ghioca

Number Theory · Submitted 15 Nov 2006

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

The authors' main claim We show that the intersection of $X$ with a finite rank $\phi$-submodule of $\mathbb{G}_a^g$ is finite.

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arXiv IDmath/0611476 (version 1)
Pith IDL5WXE67I, Pith's permanent record of this paper and its review
CitationDragos Ghioca. "Towards the full Mordell-Lang conjecture for Drinfeld modules." arXiv:math/0611476 (2006). https://pith.science/paper/L5WXE67I
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,301 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Let $\phi$ be a Drinfeld module of generic characteristic, and let $X$ be a sufficiently generic affine subvariety of $\mathbb{G}_a^g$. We show that the intersection of $X$ with a finite rank $\phi$-submodule of $\mathbb{G}_a^g$ is finite.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let $\phi$ be a Drinfeld module of generic characteristic, and let $X$ be a sufficiently generic affine subvariety of $\mathbb{G}_a^g$. background 0.98 0.07 0.02 unclear 0.57
s1 We show that the intersection of $X$ with a finite rank $\phi$-submodule of $\mathbb{G}_a^g$ is finite. result 0.99 0.95 0.94 asserted 1.00

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

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

The paper
Original abstract

Let $\phi$ be a Drinfeld module of generic characteristic, and let $X$ be a sufficiently generic affine subvariety of $\mathbb{G}_a^g$. We show that the intersection of $X$ with a finite rank $\phi$-submodule of $\mathbb{G}_a^g$ is finite.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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