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arXiv · 1510.04383

On endomorphisms of hypersurfaces

Ilya Karzhemanov
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Abstract

For any prime $p\ge 5$, we show that generic hypersurface $X_p\subset\mathbb{P}^p$ defined over $\mathbb{Q}$ admits a non-trivial rational dominant self-map of degree $>1$, defined over $\bar{\mathbb{Q}}$. A simple arithmetic application of this fact is also given.

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Ilya Karzhemanov. 2017-02-08. On endomorphisms of hypersurfaces. https://arxiv.org/abs/1510.04383

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