2 problems

Let $X$ and $X'$ be seminormal, geometrically irreducible varieties over fields $k$ and $k'$, respectively, with $\noperatorname{char} k=0$ and $dim Xgeq 2$. A homeomorphism … is…

Uniqueness conjecture. If the reconstruction problem has more than one solution up to homeomorphism, then trivial clans rooted at $k$-sets for some $k<n-1$ must exist.