Decomposition of the diagonal and eigenvalues of Frobenius for Fano hypersurfaces

Spencer Bloch, Hélène Esnault, Marc Levine

Let $X\subset {\P }^n$ be a possibly singular hypersurface of degree $d\le n$, defined over a finite field $k$. We show that the diagonal, suitably interpreted, is decomposable. This g…