Cycles for rational maps with good reduction outside a prescribed set
| dc.creator | Canci, J. K. | |
| dc.date | 2005-04-26 | |
| dc.date | 2006-07-17 | |
| dc.date.accessioned | 2026-07-07T06:39:51Z | |
| dc.date.available | 2026-07-07T06:39:51Z | |
| dc.description | Let $K$ be a number field and $S$ a fixed finite set of places of $K$ containing all the archimedean ones. Let $R_S$ be the ring of $S$-integers of $K$. In the present paper we study the cycles for rational maps of $\mathbb{P}_1(K)$ of degree $\geq2$ with good reduction outside $S$. We say that two ordered $n$-tuples $(P_0,P_1,...,P_{n-1})$ and $(Q_0,Q_1,...,Q_{n-1})$ of points of $\mathbb{P}_1(K)$ are equivalent if there exists an automorphism $A\in{\rm PGL}_2(R_S)$ such that $P_i=A(Q_i)$ for every index $i\in\{0,1,...,n-1\}$. We prove that if we fix two points $P_0,P_1\in\mathbb{P}_1(K)$, then the number of inequivalent cycles for rational maps of degree $\geq2$ with good reduction outside $S$ which admit $P_0,P_1$ as consecutive points is finite and depends only on $S$. We also prove that this result is in a sense best possible. | |
| dc.description | 30 pages, changed content | |
| dc.identifier | https://arxiv.org/abs/math/0504533 | |
| dc.identifier | http://arxiv.org/abs/math/0504533 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101230 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G99 (Primary) 14E05 (Secondary) | |
| dc.title | Cycles for rational maps with good reduction outside a prescribed set | |
| dc.type | text |