Osaka Journal of Mathematics

Equations in $p$-curvature and intertwiners

Yoshifumi Tsuchimoto

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The equations in $p$-curvatures, which is a key to prove a stable equivalence of Jacobian problem and Dixmier conjecture in the author's previous paper, is provided an easier proof, related to the existence of `intertwining operator'. In an appendix, we show that every symplectic morphism between nonsingular symplectic varieties are of Jacobian 1, regardless of the characteristics.

Article information

Osaka J. Math., Volume 45, Number 3 (2008), 737-746.

First available in Project Euclid: 17 September 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R15: Jacobian problem [See also 13F20]
Secondary: 14A22: Noncommutative algebraic geometry [See also 16S38]


Tsuchimoto, Yoshifumi. Equations in $p$-curvature and intertwiners. Osaka J. Math. 45 (2008), no. 3, 737--746.

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  • N. Jacobson: Lie Algebras, Interscience Publishers, New York, 1962.
  • N.M. Katz: Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. 39 (1970), 175--232.
  • N.M. Katz: Algebraic solutions of differential equations ($p$-curvature and the Hodge filtration), Invent. Math. 18 (1972), 1--118.
  • S. Lang: Algebra, revised third edition, Graduate Texts in Mathematics 211, Springer, New York, 2002.
  • Y. Tsuchimoto: Preliminaries on Dixmier conjecture, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 24 (2003), 43--59.
  • Y. Tsuchimoto: Endomorphisms of Weyl algebra and $p$-curvatures, Osaka J. Math. 42 (2005), 435--452.
  • Y. Tsuchimoto: Non commutative algebraic spaces of finite type over Dedekind domains, J. Math. Kyoto Univ. 46 (2006), 553--582.