Abstract
We prove new theorems that are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. These include results on integral points over varying number fields of bounded degree and results on Kobayashi hyperbolicity. We give a number of new conjectures describing, from our point of view, how we expect Siegel’s and Picard’s theorems to optimally generalize to higher dimensions.
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[Co]
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ISSN = {1474-7480},
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MRNUMBER = {2005m:11055},
DOI = {10.1017/S1474748005000071},
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@article{Za, MRKEY = {0141668},
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FJOURNAL = {Annals of Mathematics. Second Series},
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MRNUMBER = {25 \#5065},
DOI = {10.2307/1970376},
ZBLNUMBER = {0124.37001},
MRREVIEWER = {Y. Nakai},
}
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