10 problems

Finiteness conjecture. These groups are finite. This conjecture is introduced to obtain finite-generation consequences for motivic cohomology when combined with the etale realizati…

Finiteness conjecture. For $l\geq 1$ and $\mathop{\cal B}\nolimits$ as above, $o(\mathop{\cal B}\nolimits)$ is always finite.

Let $\overline{\mathcal{H}}_{\geq 7}(2,1)$ denote the set defined in the paper, consisting of the relevant heavenly elliptic-curve data over quadratic fields with prime parameter a…

Strong finiteness conjecture. There is a family

Pointed Shafarevich conjecture. The set of morphisms $f:C\to U$ satisfying $f(c)=u$ is finite. This predicts finiteness of families over a curve after fixing one fibre over one mar…

Let $X$ be a proper variety over $\mathbb{C}$ and let $Y$ be a projective integral variety over $\mathbb{C}$. A pseudo-Brody hyperbolic variety is a variety that is Brody hyperboli…

Let $d,k$ be positive integers. For an ordered matroid $M$, write $\overline{BC_<(M)}$ for its reduced broken circuit complex, and let $h_{d-1}(\overline{BC_<(M)})$ denote its…

Fix nonnegative integers $h^{r,w-r}$ as above and a set $S$ of prime numbers. Let $F$ be the underlying number field, let $w$ be the weight, and let $M$ be a pure $\mathbb Z$-motiv…

Let $k$ be a $\sigma$-field and $R$ a finitely $\sigma$-generated $k$-$\sigma$-algebra. A prime … of $R$ is minimal if every prime … with $\subset$ satisfies $=$. Minimal-prime fin…

Let $m$ be a natural number, and consider polynomials of the form … Here ${\lambda}$ and ${\nu}$ range over the indexing partitions and $p(1)$ is the ordinary Kostka coefficient at…