On the Jung method in positive characteristic

Piltant, Olivier

doi:10.5802/aif.1978

Cited by 7 publications

(8 citation statements)

References 11 publications

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“…Let H j be the subgroup of G r 0 generated by G r and H j , 0 j α. Eq. (35) implies that H j is invariant in H j +1 and that H j +1 /H j is a quotient of H j +1 /H j Z/p. By Galois correspondence, the extension K r /K r 0 is a tower of Galois extensions of degree p. As in the purely inseparable case, the local uniformization in each intermediate extension of this tower is handled by Proposition 6.3 (nonimmediate case) or by assumption in the statement of the theorem (immediate case).…”

Section: Abhyankar's Strategy: Reduction To Artin-schreier and Purelymentioning

confidence: 91%

Resolution of singularities of threefolds in positive characteristic. I.

2008

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Section: Abhyankar's Strategy: Reduction To Artin-schreier and Purelymentioning

confidence: 91%

Resolution of singularities of threefolds in positive characteristic. I.

2008

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“…Each R i has allowable regular parameters (x i , y i ) and (x i , y i ) and each S i has allowable regular parameters (u i , v i ) and (u i , v i ). The map S i → S i+1 is defined by (30) x…”

Section: Switching Of Types Of Extensions Under Blowing Upmentioning

confidence: 99%

Erratic birational behavior of mappings in positive characteristic

Cutkosky¹

2021

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Birational properites of generically finite morphisms X → Y of algebraic varieties can be understood locally by a valuation of the function field of X. In finite extensions of algebraic local rings in characteristic zero algebraic function fields which are dominated by a valuation there are nice monomial forms of the mapping after blowing up enough, which reflect classical invariants of the valuation. Further, these forms are stable upon suitable further blowing up. In positive characteristic algebraic function fields it is not always possible to find a monomial form after blowing up along a valuation, even in dimension two. In dimension two and positive characteristic, after enough blowing up, there are stable forms of the mapping which hold upon suitable sequences of blowing.We give examples showing that even within these stable forms, the forms can vary dramatically (erratically) upon further blowing up. We construct these examples in towers of defect Artin-Schreier extensions which can have any prescribed distance.

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“…This last result suggests that embedded resolution of singularities should hold, at least for 3-dimensional schemes over perfect fields. More results concerning resolution of singularities in positive characteristic can be found in [1,3,7,16,25,26,[28][29][30]38,39,42,43,48].…”

Section: Sections 2 and 3 Include An Overview Of Invariants That Havementioning

confidence: 99%