Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"

Jeffrey Katen; Mihran Papikian; Valentijn Karemaker

arxiv: 2606.05223 · v1 · pith:DPVLHXQYnew · submitted 2026-06-01 · 🧮 math.NT

Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"

Valentijn Karemaker , Jeffrey Katen , Mihran Papikian This is my paper

Pith reviewed 2026-06-28 12:55 UTC · model grok-4.3

classification 🧮 math.NT

keywords Drinfeld modulesfinite fieldsisomorphism classescorrigendumarithmetic geometry

0 comments

The pith

A correction to Theorem 5.4 keeps the main theorems on Drinfeld module isomorphisms valid as stated.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This note corrects an error in Theorem 5.4 of the earlier paper on isomorphism classes of Drinfeld modules over finite fields. It supplies a replacement theorem to fix the issue in the argument. The main Theorems A and B remain valid without any change to their statements. Only the proof of Theorem B needs to be updated by using the new theorem in place of the original one.

Core claim

Theorem 5.4 of the original paper contains an error and is replaced by a corrected version; this substitution modifies the proof of Theorem B but leaves the statements of Theorems A and B intact and correct.

What carries the argument

The replacement theorem for the original Theorem 5.4 that supplies the needed step in the classification argument.

If this is right

The statements of Theorems A and B on isomorphism classes remain unchanged.
The proof of Theorem B is now valid after the substitution.
The classification of Drinfeld modules over finite fields holds as originally described.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The error was limited to one supporting theorem and did not affect the overall conclusions.
Readers applying the main results can do so using the corrected reference.

Load-bearing premise

The new theorem correctly fills the role of the erroneous Theorem 5.4 in the proof of Theorem B.

What would settle it

An explicit Drinfeld module over a finite field whose isomorphism class contradicts the statement of Theorem B after the correction is applied would show the claim is false.

read the original abstract

In this note we provide corrections to Theorem 5.4 of the paper ``Isomorphism classes of Drinfeld modules over finite fields'', arXiv:2209.15033. The main theorems of this paper, Theorem A and B in its introduction, are valid as stated; in the proof of Theorem B the argument needs to be modified by replacing the erroneous Theorem 5.4 by the theorem of this note.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a narrow correction that replaces one erroneous theorem while keeping the main results intact.

read the letter

This corrigendum corrects an error in Theorem 5.4 of the 2022 paper on isomorphism classes of Drinfeld modules over finite fields. The authors state that the main theorems A and B remain valid, with only a modification needed in the proof of Theorem B by using the new theorem instead of the old one.

The note does a solid job of being precise about the scope of the change. It identifies the problem directly and provides the replacement without claiming any wider implications. This kind of targeted correction is important for keeping mathematical literature reliable.

What is new here is just the corrected statement of that one theorem. There are no fresh derivations, examples, or applications. The work is entirely about rectifying the prior mistake.

A soft spot is that the broader impact is quite narrow. Even a correct fix in this area of number theory will not affect many researchers outside the subfield. The assumption that the new theorem works as a drop-in replacement seems plausible based on the abstract, but without the full details of both the error and the fix, it is difficult to judge if any other parts of the original proofs might be affected.

The citation pattern is appropriate since it refers back to the original paper. There is no attempt to overstate the contribution.

This paper is intended for specialists who are familiar with the 2022 work and may have relied on Theorem 5.4 in their own research or reading. For them, having the correction available is practical.

It deserves peer review to ensure the replacement theorem is accurate and that the modification to the proof of Theorem B is sufficient. I would recommend sending it out rather than rejecting it outright.

Referee Report

0 major / 1 minor

Summary. This short corrigendum corrects an error in Theorem 5.4 of the 2022 paper 'Isomorphism classes of Drinfeld modules over finite fields' (arXiv:2209.15033). It states that the main results, Theorems A and B from the introduction of the original paper, remain valid as stated; the proof of Theorem B requires only the substitution of the corrected statement for the original Theorem 5.4.

Significance. The note restores the validity of the central claims on isomorphism classes of Drinfeld modules over finite fields by supplying a replacement for the flawed theorem. Because the original paper's main theorems are asserted to hold after this local change, the corrigendum directly supports the reliability of results in the arithmetic of function fields.

minor comments (1)

The note does not reproduce the statement of the corrected theorem in full; including the precise new statement (or at least its key differences from the original Theorem 5.4) would make the replacement self-contained for readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the corrigendum and for recommending acceptance. The note provides the necessary correction to Theorem 5.4 while preserving the validity of Theorems A and B.

Circularity Check

0 steps flagged

No significant circularity; direct correction of prior error

full rationale

This corrigendum explicitly identifies an error in Theorem 5.4 of the authors' prior paper and supplies a replacement theorem, stating that Theorems A and B remain valid after the substitution in the proof of B. No derivation is presented that reduces by construction to its own inputs, no fitted parameter is renamed as a prediction, and no load-bearing uniqueness claim rests on an unverified self-citation chain. The note is a targeted, self-contained fix whose central assertion is the sufficiency of the replacement, with no internal reduction to the inputs being corrected.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The corrigendum relies on standard axioms of algebraic number theory and Drinfeld module theory from the prior literature without new parameters or entities.

pith-pipeline@v0.9.1-grok · 5593 in / 853 out tokens · 31100 ms · 2026-06-28T12:55:37.293540+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 5 canonical work pages

[1]

2025 , eprint=

Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms , author=. 2025 , eprint=

2025
[2]

Mathematika , volume =

de Vries, Sjoerd , title =. Mathematika , volume =. doi:https://doi.org/10.1112/mtk.70077 , year =

work page doi:10.1112/mtk.70077
[3]

Garai, Sumita and Papikian, Mihran , TITLE =. J. Number Theory , FJOURNAL =. 2022 , PAGES =. doi:10.1016/j.jnt.2019.11.018 , URL =

work page doi:10.1016/j.jnt.2019.11.018 2022
[4]

1992 , PAGES =

Greither, Cornelius , TITLE =. 1992 , PAGES =. doi:10.1007/BFb0089165 , URL =

work page doi:10.1007/bfb0089165 1992
[5]

, TITLE =

Hayes, D. , TITLE =. Studies in algebra and number theory , SERIES =
[6]

Karemaker, Valentijn and Katen, Jeffrey and Papikian, Mihran , TITLE =. J. Algebra , FJOURNAL =. 2024 , PAGES =

2024
[7]

, TITLE =

Laumon, G. , TITLE =. 1996 , PAGES =

1996
[8]

2023 , PAGES =

Papikian, Mihran , TITLE =. 2023 , PAGES =. doi:10.1007/978-3-031-19707-9 , URL =

work page doi:10.1007/978-3-031-19707-9 2023
[9]

, TITLE =

Waterhouse, William C. , TITLE =. Ann. Sci. \'. 1969 , PAGES =

1969
[10]

Yu, Jiu-Kang , TITLE =. J. Number Theory , FJOURNAL =. 1995 , NUMBER =. doi:10.1006/jnth.1995.1108 , URL =

work page doi:10.1006/jnth.1995.1108 1995

[1] [1]

2025 , eprint=

Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms , author=. 2025 , eprint=

2025

[2] [2]

Mathematika , volume =

de Vries, Sjoerd , title =. Mathematika , volume =. doi:https://doi.org/10.1112/mtk.70077 , year =

work page doi:10.1112/mtk.70077

[3] [3]

Garai, Sumita and Papikian, Mihran , TITLE =. J. Number Theory , FJOURNAL =. 2022 , PAGES =. doi:10.1016/j.jnt.2019.11.018 , URL =

work page doi:10.1016/j.jnt.2019.11.018 2022

[4] [4]

1992 , PAGES =

Greither, Cornelius , TITLE =. 1992 , PAGES =. doi:10.1007/BFb0089165 , URL =

work page doi:10.1007/bfb0089165 1992

[5] [5]

, TITLE =

Hayes, D. , TITLE =. Studies in algebra and number theory , SERIES =

[6] [6]

Karemaker, Valentijn and Katen, Jeffrey and Papikian, Mihran , TITLE =. J. Algebra , FJOURNAL =. 2024 , PAGES =

2024

[7] [7]

, TITLE =

Laumon, G. , TITLE =. 1996 , PAGES =

1996

[8] [8]

2023 , PAGES =

Papikian, Mihran , TITLE =. 2023 , PAGES =. doi:10.1007/978-3-031-19707-9 , URL =

work page doi:10.1007/978-3-031-19707-9 2023

[9] [9]

, TITLE =

Waterhouse, William C. , TITLE =. Ann. Sci. \'. 1969 , PAGES =

1969

[10] [10]

Yu, Jiu-Kang , TITLE =. J. Number Theory , FJOURNAL =. 1995 , NUMBER =. doi:10.1006/jnth.1995.1108 , URL =

work page doi:10.1006/jnth.1995.1108 1995