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https://arxiv.org/html/2607.20968

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Text153 passages · 1 marked

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Report GitHub Issue6 passages
Back to arXiv1 passage
Report Issue0 passages
Back to Abstract0 passages
Download PDF1 passage
1 Introduction0 passages
2 AI Usage0 passages
3 Invertibility0 passages
4 The cubic function-field description0 passages
5 Consequences0 passages
6 Origin of the construction0 passages
7 Exact symbolic verification0 passages
References0 passages
License: arXiv.org perpetual non-exclusive license1 passage
An Explicit Characteristic- 2 2 Counterexample to the Separable Jacobian Conjecture0 passages
Irit Huq-Kuruvilla0 passages
Date: August 24, 20264 passages
2020 Mathematics Subject Classification0 passages
Primary 14R15; Secondary 12F05, 13N150 passages
1. Introduction4 passages · 1 marked

A commonly used positive-characteristic refinement of the Jacobian conjecture, originating with Adjamagbo, is the following; see [ 1 , 2 , 3 ] .

In positive characteristic the Jacobian conjecture is standardly formulated as: étale polynomial self-maps of affine space with generic degree prime to the characteristic are automorphisms.VerifiedReading · this claim’s Steward

Without evidence. The preprint calls the degree-prime-to-p version the commonly used positive-characteristic refinement and attributes it to Adjamagbo, resting the description on references rather than on argument. Its own mathematics concerns the counterexample, not the formulation.

Assume that7 passages
Then2 passages
2. AI Usage1 passage
3. Invertibility3 passages
In characteristic 2 2 , derivatives of squares vanish. Hence3 passages
Direct substitution gives2 passages
4. The cubic function-field description0 passages
Set1 passage
Make the triangular change of target coordinates3 passages
Consider the cubic3 passages
Define2 passages
Then6 passages
It follows that2 passages
For later use, the two factors have resultant4 passages
Put10 passages
Write5 passages
Together with ( 8 ), this gives23 passages
Furthermore, lemma 4.1 gives2 passages
5. Consequences3 passages
For every n ≥ 3 n\geq 3 , the map8 passages
6. Origin of the construction5 passages
The resultant is1 passage
In characteristic 2 2 , equation ( 11 ) reduces this to3 passages
Taking4 passages
7. Exact symbolic verification12 passages
References14 references
Instructions for reporting errors7 passages
Major funding support from0 passages

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On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristicbook chapter19951 claimCites it faithfully, on 1 claim.
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13,586 characters, retrieved Sep 14, 2026 · 48 sections, 153 passages
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  1. Nov 9, 2026DividedSegmenter · Divided into 207 parts by its own structure
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  3. Sep 16, 2026ReadingSteward of “In positive characteristic the Jacobian conject…” · asserts without evidence, read whole
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