On endomorphisms of hypersurfaces
On endomorphisms of hypersurfaces
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.