2014 / December Volume 9 No.4
Deviations from $S$-Integrality in Orbits on $P^N$
| Published Date |
2014 / December
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|---|---|
| Title | Deviations from $S$-Integrality in Orbits on $P^N$ |
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| Download | |
| Pagination | 603-632 |
| Abstract | Silverman proved that when the second iterate of a rational function $\varnothing$ is not a polynomial, there are only finitely many $S$-integral points in each orbit of a rational point. We will survey prior results that attempt to generalize this result to higher-dimensions, and then we will discuss an improvement of them. All of these general theories assume some version of a very deep Diophantine conjecture by Vojta. We will also give some examples of maps for which these general theories do not apply directly but for which deviations from $S$-integrality in orbits can be analyzed unconditionally. We will end by posing many questions still to be answered.
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| AMS Subject Classification |
37P55, 11J97, 37P15
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| Received |
2014-07-07
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| Accepted |
2014-07-16
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