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A new formulation of the Jacobian Conjecture in characteristic $p$

Volume 146 / 2017

Stefan Maubach, Abdul Rauf Colloquium Mathematicum 146 (2017), 15-30 MSC: Primary 14R15; Secondary 13F20. DOI: 10.4064/cm6692-3-2016 Published online: 11 July 2016

Abstract

The Jacobian Conjecture uses the equation $\mathop {\rm det}\mathop {\rm Jac}(F)\in k^*$, which is a very short way to write down many equations putting restrictions on the coefficients of a polynomial map $F$. In characteristic $p$ these equations do not suffice to (conjecturally) force a polynomial map to be invertible. We describe how to construct the conjecturally sufficient equations in characteristic $p$ forcing a polynomial map to be invertible. This provides a formulation of the Jacobian Conjecture in characteristic $p$, alternative to Adjamagbo’s. We strengthen this formulation by investigating some special cases and by linking it to the regular Jacobian Conjecture in characteristic zero.

Authors

  • Stefan MaubachRadboud University Nijmegen
    Postbus 9010
    6500 GL Nijmegen, The Netherlands
    e-mail
  • Abdul RaufDepartment of Mathematics
    Jacobs University Bremen
    Bremen, Germany
    e-mail

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