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The invariant of $PGU(3,q)$ in the Hermitian function field

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Gatti Barbara, Ghiandoni Francesco, Gábor Korchmáros

Number Theory · Submitted 21 Dec 2023

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

The authors' main claim We determine the invariant of $Aut(\mathbb{K}(\mathcal{H}_q))\cong PGU(3,q)$, and discuss some related questions on Galois subcovers of maximal curves over finite fields.

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arXiv ID2312.13751 (version 1)
Pith IDH5UP7MIG, Pith's permanent record of this paper and its review
CitationG\'abor Korchm\'aros, Gatti Barbara, Ghiandoni Francesco. "The invariant of $PGU(3,q)$ in the Hermitian function field." arXiv:2312.13751 (2023). https://pith.science/paper/H5UP7MIG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,564 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let $F=F|\mathbb{K}$ a be function field over an algebraically closed constant field $\mathbb{K}$ of positive characteristic $p$. For a $\mathbb{K}$-automorphism group $G$ of $F$, the invariant of $G$ is the fixed field $F^G$ of $G$. If $F$ has transendency degree $1$ (i.e. $F$ is the function field of an irreducible curve) and $F^G$ is rational, then each generator of $F^G$ uniquely determines $F^G$ and it makes sense to call each of them the invariant of $G$. In this paper, $F$ is the Hermitian function field $\mathbb{K}(\mathcal{H}_q)=\mathbb{K}(x,y)$ with $y^q+y-x^{q+1}=0$ and $q=p^r$. We determine the invariant of $Aut(\mathbb{K}(\mathcal{H}_q))\cong PGU(3,q)$, and discuss some related questions on Galois subcovers of maximal curves over finite fields.

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 $F=F|\mathbb{K}$ a be function field over an algebraically closed constant field $\mathbb{K}$ of positive characteristic $p$. background 1.00 0.06 0.01 asserted 0.80
s1 For a $\mathbb{K}$-automorphism group $G$ of $F$, the invariant of $G$ is the fixed field $F^G$ of $G$. background 1.00 0.04 0.02 asserted 1.00
s2 If $F$ has transendency degree $1$ (i.e. $F$ is the function field of an irreducible curve) and $F^G$ is rational, then each generator of $F^G$ uniquely determines $F^G$ and it makes sense to call each of them the invariant of $G$. background 1.00 0.06 0.03 asserted 0.98
s3 In this paper, $F$ is the Hermitian function field $\mathbb{K}(\mathcal{H}_q)=\mathbb{K}(x,y)$ with $y^q+y-x^{q+1}=0$ and $q=p^r$. background 0.67 0.22 0.04 asserted 1.00
s4 We determine the invariant of $Aut(\mathbb{K}(\mathcal{H}_q))\cong PGU(3,q)$, and discuss some related questions on Galois subcovers of maximal curves over finite fields. contribution 0.94 0.96 0.86 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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  • references and citing sentences
  • relations to other papers
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  • P abstract
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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

Let $F=F|\mathbb{K}$ a be function field over an algebraically closed constant field $\mathbb{K}$ of positive characteristic $p$. For a $\mathbb{K}$-automorphism group $G$ of $F$, the invariant of $G$ is the fixed field $F^G$ of $G$. If $F$ has transendency degree $1$ (i.e. $F$ is the function field of an irreducible curve) and $F^G$ is rational, then each generator of $F^G$ uniquely determines $F^G$ and it makes sense to call each of them the invariant of $G$. In this paper, $F$ is the Hermitian function field $\mathbb{K}(\mathcal{H}_q)=\mathbb{K}(x,y)$ with $y^q+y-x^{q+1}=0$ and $q=p^r$. We determine the invariant of $Aut(\mathbb{K}(\mathcal{H}_q))\cong PGU(3,q)$, and discuss some related questions on Galois subcovers of maximal curves over finite fields.

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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

What it cites

Cites as background 1 paper
  • The study of modular invariants was initiated in the 1910s by the pioneering work of Dickson and it is still an active research area also in connection with the study of Chern classes; see for instance [ref] .

    2306.17599 · Introduction · 0.98

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