2014 / December Volume 9 No.4
A Bogomolov Type Statement for Functions Fields
| Published Date |
2014 / December
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| Title | A Bogomolov Type Statement for Functions Fields |
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| Download | |
| Pagination | 641-656 |
| Abstract | Let $ \ k \ $ be a an algebraically closed field of arbitrary characteristic, and we let $h:\mathbb{A}^n(\overline{k(t)})\longrightarrow \mathbb{R}_{\ge 0}$ be the usual Weil height for the $n$-dimensional affine space corresponding to the function field $k(t)$ (extended to its algebraic closure). We prove that for any affine variety $V\subset \mathbb{A}^n$ defined over $\overline{k(t)}$, there exists a positive real number $\epsilon:=\epsilon(V)$ such that if $P\in V(\overline{k(t)})$ and $h(P)<\epsilon$, then $P\in V(k)$.
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| AMS Subject Classification |
11G50, 14G17, 11G10.
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| Received |
2014-02-15
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| Accepted |
2014-02-27
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