Some Remarks on the Jacobian Conjecture and Connections with Hilbert's Irreducibility Theorem

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dc.creatorLipton, Richard J.
dc.creatorMarkakis, Evangelos
dc.date2005-07-26
dc.date.accessioned2026-07-07T05:21:59Z
dc.date.available2026-07-07T05:21:59Z
dc.descriptionWe make two observations regarding the invertibility of Keller maps. i.e., polynomial maps for which the determinant of their Jacobian matrix is identically equal to 1. In our first result, we show that if P is a n-dimensional Keller map, defined over any extension of Q, then P has a polynomial inverse if and only if the range of P contains the cartesian product of n universal Hilbert sets. In our second result, we show that if P is a 2-dimensional Keller map, defined over any algebraic number field, then P is invertible on a set that contains almost all rational integers of K.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0507525
dc.identifierhttp://arxiv.org/abs/math/0507525
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75896
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject14R15
dc.titleSome Remarks on the Jacobian Conjecture and Connections with Hilbert's Irreducibility Theorem
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