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On the Modularity of Wildly Ramified Galois Representations

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Edray Herber Goins

Number Theory · Submitted 9 Nov 2004

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

The authors' main claim We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples.

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arXiv IDmath/0411214 (version 1)
Pith IDYFG4GNKE, Pith's permanent record of this paper and its review
CitationEdray Herber Goins. "On the Modularity of Wildly Ramified Galois Representations." arXiv:math/0411214 (2004). https://pith.science/paper/YFG4GNKE
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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, 2,939 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.74 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the original example studied by Buhler. In the process, we prove that an infinite family of residually modular Galois representations are modular by studying $\Lambda$-adic Hecke algebras.

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 show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. result 0.93 0.96 0.95 asserted 1.00
s1 Such a family contains the original example studied by Buhler. result 0.61 0.22 0.04 asserted 1.00
s2 In the process, we prove that an infinite family of residually modular Galois representations are modular by studying $\Lambda$-adic Hecke algebras. result 0.60 0.95 0.10 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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  • 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

We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the original example studied by Buhler. In the process, we prove that an infinite family of residually modular Galois representations are modular by studying $\Lambda$-adic Hecke algebras.

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