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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Operators with nilpotent $ p$-curvature


Author: Hans Schmitt
Journal: Proc. Amer. Math. Soc. 119 (1993), 701-710
MSC: Primary 12H05; Secondary 14M10, 34A99
MathSciNet review: 1158007
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Abstract: This article studies the variety of nilpotent $ p$-curvature of linear differential operators on the sphere with $ m + 1$ singularities. We shall show that for a given set of exponents $ \in {{\mathbf{F}}_p}$ satisfying Fuchs's relation the associated variety of nilpotent $ p$-curvature is a nonempty complete intersection of dimension, essentially, $ m - 2$. The subject has previously been studied by Katz, Honda, and Dwork.


References [Enhancements On Off] (What's this?)

  • [Dw] Bernard Dwork, Differential operators with nilpotent 𝑝-curvature, Amer. J. Math. 112 (1990), no. 5, 749–786. MR 1073008, 10.2307/2374806
  • [Ho] Taira Honda, Algebraic differential equations, Symposia Mathematica, Vol. XXIV (Sympos., INDAM, Rome, 1979) Academic Press, London-New York, 1981, pp. 169–204. MR 619247
  • [Ka] Nicholas M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. 39 (1970), 175–232. MR 0291177

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1158007-1
Keywords: Nilpotent $ p$-curvature, linear differential operators, moduli space
Article copyright: © Copyright 1993 American Mathematical Society