A generalised Skolem-Mahler-Lech theorem for affine varieties
| dc.creator | Bell, Jason P. | |
| dc.date | 2005-01-20 | |
| dc.date | 2007-09-15 | |
| dc.date.accessioned | 2026-07-07T08:29:24Z | |
| dc.date.available | 2026-07-07T08:29:24Z | |
| dc.description | The 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.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0501309 | |
| dc.identifier | http://arxiv.org/abs/math/0501309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137955 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11D45; 14R10; 11Y55 | |
| dc.title | A generalised Skolem-Mahler-Lech theorem for affine varieties | |
| dc.type | text |