On endomorphisms of hypersurfaces

Ilya Karzhemanov

Published 2015-10-15Version 1

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.