On endomorphisms of hypersurfaces (Q1689867)

The author studies hypersurfaces in projective space whose endomorphism ring contains non-trivial elements. His main result states that for any prime \(p\geq 5\), general \(\mathbb{Q}\)-hypersurface \(\mathbb{X}_p \subset \mathbb{P}^{p}\) admits an endomorphism \( f_{\mathbb{X}_p}\) of degree greater than \(1\), defined over \(\bar{\mathbb{Q}}\).