On a discrepancy among Picard-Vessiot theories in positive characteristics

Details On a discrepancy among Picard-Vessiot theories in positive characteristics On a discrepancy among Picard-Vessiot theories in positive characteristics

2006-12-22

arxiv.org/abs/math/0612683v2

Mathematics

Commutative Algebra

10 pages; an informal research note; [v1->v2] Some unnecessary sentences (in page 1, page 5, etc) are removed

Scientific paper

There is a serious discrepancy among literature on the Picard-Vessiot theory in positive characteristics (for iterative differential fields). It is about descriptions of Galois correspondence. We should use affine group schemes instead of algebraic matrix groups to obtain a suitable Galois correspondence. If one adheres to algebraic matrix groups, then his correspondence may not be bijective.

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