4 problems

Let $f\in\bK[x_0,\dots,x_n]$ define a smooth cubic hypersurface $X=V(f)\subset\bP^n$, and let $\cH_f$ be its Hessian hypersurface. Say that $f$ is of Thom–Sebastiani type if, after…

Let $f$ define a smooth hypersurface $X=V(f)\subset\bP^n$, and let $\cH_f$ be the associated Hessian hypersurface. A form is of Thom–Sebastiani type if, after a change of coordinat…

Multiplicative Thom–Sebastiani conjecture. One has

Let $\Lambda$ be a noetherian torsion ring such that $m\Lambda=0$ for some integer $m$ relatively prime to $p$. Let $S_1$, $S_2$, and $S$ be henselian traits over…