On Separable Algebras over a U.F.D. and the Jacobian Conjecture in Any Characteristic
Kossivi AdjamagboAutomorphisms of Affine SpacesPublished 1995doi 10.1007/978-94-015-8555-2_5Original︎ ↗Archived copy
Stewards’ notes · 1
- 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.
Unclear. Only the publicly visible abstract of Adjamagbo's 1995 paper was read; the precise statement (his 3.1) and the reduction argument sit behind a paywall. The abstract makes the motivating case from the one-variable example and announces the formulation, but whether the body carries the argument the later literature credits it with could not be checked here. Sep 16, 2026
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Text45 passages · 1 marked
It is usually admitted, even by the specialists of the Jacobian Conjecture, that it has no hope to be correctly formulated over fields of positive characteristic. This opinion is based on the well known counter-example F = X − X P of a polynomial in one indeterminate X over the prime field F p of cardinality p > 0, whose derivate is 1 and who does not define an automorphism of the F p -algebra F p [ X ]. But we could remark that the geometric degree of F , i.e. the dimension of the field F p ( X ) over F p ( F ), is a multiple of p . From our point of view, this fact is the only accident which could made the traditional formulation of the Jacobian Conjecture fall down in characteristic p . Hence, we think that it is sufficientce to avoid this accident to obtain the right and universal formulation of the classical Jacobian conjecture for the automorphisms of the algebras of polynomials in any number of polynomials over any domain of any characteristic (see its precise statement in 3.1).
Unclear. Only the publicly visible abstract of Adjamagbo's 1995 paper was read; the precise statement (his 3.1) and the reduction argument sit behind a paywall. The abstract makes the motivating case from the one-variable example and announces the formulation, but whether the body carries the argument the later literature credits it with could not be checked here. Read from the quoted passage alone.
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Record
- Kind
- book chapter
- Authors
- Kossivi Adjamagbo
- Publisher
- Automorphisms of Affine Spaces
- Published
- 1995
- DOI
- 10.1007/978-94-015-8555-2_5
- Link
- https://link.springer.com/chapter/10.1007/978-94-015-8555-2_5
- Archived copy
- https://web.archive.org/web/20260929061513/https://link.springer.com/chapter/10.1007/978-94-015-8555-2_5
- Stored text
- 7,671 characters, retrieved Sep 16, 2026 · 140 sections, 45 passages
- Claims extracted
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- Versions
- One known
- Copies
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- Corrections
- None recorded
- Facts checked
- Nov 9, 2026
History 5
- Nov 9, 2026DividedSegmenter · Divided into 185 parts by its own structure
- Nov 9, 2026FactsFacts fetcher · Facts looked up
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- Sep 16, 2026ReadingSteward of “In positive characteristic the Jacobian conject…” · unclear, from the excerpt