A generalised Skolem-Mahler-Lech theorem for affine varieties

dc.creatorBell, Jason P.
dc.date2005-01-20
dc.date2007-09-15
dc.date.accessioned2026-07-07T08:29:24Z
dc.date.available2026-07-07T08:29:24Z
dc.descriptionThe Skolem-Mahler-Lech theorem states that if $f(n)$ is a sequence given by a linear recurrence over a field of characteristic 0,then the set of $m$ such that $f(m)$ is equal to 0 is the union of a finite number of arithmetic progressions in $m\ge 0$ and a finite set. We prove that if $X$ is a subvariety of an affine variety $Y$ over a field of characteristic 0 and ${\bf q}$ is a point in $Y$, and $σ$ is an automorphism of $Y$, then the set of $m$ such that $σ^m({\bf q})$ lies in $X$ is a union of a finite number of complete doubly-infinite arithmetic progressions and a finite set. We show that this is a generalization of the Skolem-Mahler-Lech theorem.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0501309
dc.identifierhttp://arxiv.org/abs/math/0501309
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137955
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11D45; 14R10; 11Y55
dc.titleA generalised Skolem-Mahler-Lech theorem for affine varieties
dc.typetext

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