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Non-elliptic Shimura curves of genus one

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Josep Gonzalez, Victor Rotger

Number Theory · Submitted 23 Dec 2006

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

The authors' main claim We present explicit models for non-elliptic genus one Shimura curves X_0(D, N) with Gamma_0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them.

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arXiv IDmath/0612732 (version 2)
Pith IDWSXOHZES, Pith's permanent record of this paper and its review
CitationJosep Gonzalez, Victor Rotger. "Non-elliptic Shimura curves of genus one." arXiv:math/0612732 (2006). https://pith.science/paper/WSXOHZES
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,901 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.33 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We present explicit models for non-elliptic genus one Shimura curves X_0(D, N) with Gamma_0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work in his Ph. D Thesis on points with complex multiplication on Shimura curves.

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 We present explicit models for non-elliptic genus one Shimura curves X_0(D, N) with Gamma_0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them. contribution 0.99 0.95 0.77 asserted 1.00
s1 In addition, we discuss and extend Jordan's work in his Ph. contribution 0.95 0.64 0.03 asserted 0.76
s2 D Thesis on points with complex multiplication on Shimura curves. contribution 0.83 0.33 0.04 unclear 0.79

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.98.

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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

The paper
Original abstract

We present explicit models for non-elliptic genus one Shimura curves X_0(D, N) with Gamma_0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work in his Ph. D Thesis on points with complex multiplication on Shimura curves.

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