8 problems

Nilpotency conjecture. The fundamental group $\pi_1(X)$ is virtually nilpotent.

Virtually nilpotent fundamental-group conjecture. The fundamental group $\pi_1(X)$ is virtually nilpotent.

Let $X$ be a smooth quasi-projective variety. Define the special loci … as follows: $\mathrm{Sp}_{\mathrm{sab}}(X)$ is the Zariski closure of the union of images of non-constant ra…

Extended Lang–Vojta conjecture. The following conditions are equivalent:

Let $f\colon U\to V$ be a smooth projective algebraic fiber space between smooth quasi-projective varieties, and let $F$ be its general fiber. The quasi-projective additivity conje…

Persistence conjecture. If $X$ is arithmetically hyperbolic over $k$, then its base change $X_L$ is arithmetically hyperbolic over $L$. This asserts that finiteness of integral poi…

Quasi-projective $K(π,1)$ conjecture. There exists a smooth, connected, quasi-projective Eilenberg–MacLane space $X$ such that

Let $A$ be an abelian group and let $X$ be a smooth quasi-projective variety of dimension $n$. Let … be the natural transform from Lawson homology to singular homology. Suslin's co…