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https://arxiv.org/html/1507.02946

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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.
Supports. Maubach and Rauf give Adjamagbo's statement precisely and explain why it is a natural response to the one-variable counterexample, so their account of the formulation is well grounded. They present it as one possible version rather than the definitive one, and the paper's main purpose is to propose an alternative, so this source is the best place to see the case that the standard formulation is not the only reasonable one. Sep 16, 2026

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1 Introduction0 passages

2 Initial considerations0 passages

3 A new formulation of the Jacobian Conjecture in characteristic p p0 passages

4 Basic facts0 passages

5 Two surjectivity conjectures1 passage

7 Implications of the Jacobian Conjecture among various fields3 passages

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License: arXiv.org perpetual non-exclusive license1 passage

A new formulation of the Jacobian Conjecture in characteristic p p5 passages

Abstract2 passages

1 Introduction17 passages · 1 marked

1.2 The Jacobian Conjecture

Naievely translating the Jacobian Conjecture into characteristic p p yields counterexamples, already in dimension 1 even: the map x − x p x-x^{p} is not injective but has det ( Jac ⁡ ( x − x p ) ) = 1 \det(\operatorname{Jac}(x-x^{p}))=1 . Therefore, Adjamagbo defined in [ 4 ] a possible version of the Jacobian Conjecture for fields k k with characteristic char ⁡ ( k ) = p \operatorname{char}(k)=p :

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

Supports. Maubach and Rauf give Adjamagbo's statement precisely and explain why it is a natural response to the one-variable counterexample, so their account of the formulation is well grounded. They present it as one possible version rather than the definitive one, and the paper's main purpose is to propose an alternative, so this source is the best place to see the case that the standard formulation is not the only reasonable one.

2 Initial considerations4 passages

3 A new formulation of the Jacobian Conjecture in characteristic p p16 passages

4 Basic facts2 passages

Let F ∈ ME n ⁡ ( ℤ ) F\in\operatorname{ME}_{n}(\mathbb{Z}) . Then27 passages

5 Two surjectivity conjectures48 passages

Thus2 passages

This can be rewritten as1 passage

Regardless of characteristics, T T is a tame map of the form5 passages

7 Implications of the Jacobian Conjecture among various fields92 passages

Since by definition23 passages

References13 references

Instructions for reporting errors7 passages

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Link: https://arxiv.org/html/1507.02946
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Stored text: 65,104 characters, retrieved Sep 16, 2026 · 30 sections, 276 passages
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Versions: One known
Copies: None recorded
Corrections: None recorded
Facts checked: Nov 9, 2026

History 4

Nov 9, 2026DividedSegmenter · Divided into 314 parts by its own structure
Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 16, 2026ReadingSteward of “In positive characteristic the Jacobian conject…” · supports, read whole
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