Abstract
For any prime $p \geq 5$, we show that generic hypersurface $X_{p} \subset \mathbf{P}^{p}$ defined over $\mathbf{Q}$ admits a non-trivial rational dominant self-map of degree $> 1$, defined over ${\mathbf{\bar {Q}}}$. A simple arithmetic application of this fact is also given.
Citation
Ilya Karzhemanov. "On endomorphisms of hypersurfaces." Kodai Math. J. 40 (3) 615 - 624, October 2017. https://doi.org/10.2996/kmj/1509415236
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