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On Galois Coverings of curves and their Families

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Abolfazl Mohajer

Algebraic Geometry · Submitted 25 Apr 2023

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

The authors' main claim In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism.

how it is stated · asserted 1.00 read the record →

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arXiv ID2304.12883 (version 2)
Pith IDJ3O2FWX5, Pith's permanent record of this paper and its review
CitationAbolfazl Mohajer. "On Galois Coverings of curves and their Families." arXiv:2304.12883 (2023). https://pith.science/paper/J3O2FWX5
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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, 4,962 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.03 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. The group action by the Galois group $G$, yields a decomposition of this sheaf into irreducible local systems corresponding to irreducible representations of the group $G$. If $\rho$ is such an irreducible representation, the eigensheaf $\L_{\rho}$ of $f_*(\C)$ gives rise to another useful sheaf which is related to the homology group $H_1(C,\C)$. Using this, we describe the action of the Galois group $G$ on the homology group. As a particular example, we study the Dihedral covers of $\P^1$ in some detail.

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 In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. contribution 0.89 0.89 0.31 asserted 1.00
s1 More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. method 0.91 0.65 0.03 asserted 0.93
s2 The group action by the Galois group $G$, yields a decomposition of this sheaf into irreducible local systems corresponding to irreducible representations of the group $G$. method 0.72 0.46 0.13 asserted 1.00
s3 If $\rho$ is such an irreducible representation, the eigensheaf $\L_{\rho}$ of $f_*(\C)$ gives rise to another useful sheaf which is related to the homology group $H_1(C,\C)$. method 0.66 0.68 0.09 asserted 0.99
s4 Using this, we describe the action of the Galois group $G$ on the homology group. contribution 0.78 0.89 0.14 asserted 1.00
s5 As a particular example, we study the Dihedral covers of $\P^1$ in some detail. contribution 0.99 0.92 0.06 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.55 · evidence from proof or derivation 0.98.

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
levels run
  • 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

In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. The group action by the Galois group $G$, yields a decomposition of this sheaf into irreducible local systems corresponding to irreducible representations of the group $G$. If $\rho$ is such an irreducible representation, the eigensheaf $\L_{\rho}$ of $f_*(\C)$ gives rise to another useful sheaf which is related to the homology group $H_1(C,\C)$. Using this, we describe the action of the Galois group $G$ on the homology group. As a particular example, we study the Dihedral covers of $\P^1$ in some detail.

Human review

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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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