Journal of Commutative Algebra

Differential operators on modular extensions

Matthew Wechter

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Abstract

Given a finite purely inseparable extension of positive characteristic, this paper determines necessary and sufficient conditions on the ring of relative differential operators to establish whether the extension is modular.

Article information

Source
J. Commut. Algebra, Volume 7, Number 3 (2015), 447-458.

Dates
First available in Project Euclid: 14 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1450102165

Digital Object Identifier
doi:10.1216/JCA-2015-7-3-447

Mathematical Reviews number (MathSciNet)
MR3433992

Zentralblatt MATH identifier
06523949

Subjects
Primary: 12F15: Inseparable extensions 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]

Keywords
Modular purely inseparable differential operators divided powers positive characteristic

Citation

Wechter, Matthew. Differential operators on modular extensions. J. Commut. Algebra 7 (2015), no. 3, 447--458. doi:10.1216/JCA-2015-7-3-447. https://projecteuclid.org/euclid.jca/1450102165


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References

  • Roger C. Alperin, $p$-adic binomial coefficients $\mbox{\rm mod\,} p$, Amer. Math. Month. 92 (1985), 576–578.
  • Stephen U. Chase, Infinitesimal group scheme actions on finite field extensions, Amer. J. Math. 98 (1976), 441–480.
  • Murray Gerstenhaber, The fundamental form of an inseparable extension, Trans. Amer. Math. Soc. 227 (1977), 165–184.
  • A Grothendieck, Elements de geometrie algebrique iv, Publ. Math. IHES 20 (1964), 1965.
  • H. Hasse and F.K. Schmidt, Noch eine begrndung der theorie der hheren differentialquotienten in einem algebraischen funktionenkrper einer unbestimmten (nach einer brie ichen mitteilung von F.K. Schmidt in jena), J. reine angew. Math. 177 (1937), 215–223.
  • Nathan Jacobson, Lectures in abstract algebra, III, Springer-Verlag, New York, 1975; Theory of fields and Galois theory, Second corrected printing, Grad. Texts Math. 32, Springer-Verlag, New York.
  • Yoshikazu Nakai, High order derivations, I, Osaka J. Math. 7 (1970), 1–27.
  • Günter Pickert, Eine Normalform für endliche reininseparable Körpererweiterungen, Math. Z. 53 (1950), 133–135.
  • Richard Rasala, Inseparable splitting theory, Trans. Amer. Math. Soc. 162 (1971), 411–448.
  • Moss Eisenberg Sweedler, Structure of inseparable extensions, Ann. Math. 87 (1968), 401–410.