6 problems

Let an $\Upsilon$-scheme be given, together with the collection of polynomials associated with its counting data. Greatest-common-divisor conjecture. The zeta function of an…

Unbounded global dimension conjecture. The global dimension of a general quiver might grow arbitrarily large, for example by taking values such as $3$, $4$, or $5$. The phenomenon…

Canonical realizations conjecture. The set of realizations of $M$ over $\mathbb{E}$ canonically injects into the set of $\hat{H}\mathbb{E}$-module structures on $\hat{H}M$.

Manin's conjecture. This $\Gamma$-factor should be the zeta function of the dual of $\mathbb{P}^{\infty}_{\mathbb{F}_1}$.

Let $S$ be a $\mathscr{D}_0$-scheme, and let $\overline{S}$ be a $\mathbb{Z}$-scheme descending to $S$. Suppose that $S$ has a counting polynomial $X$ satisfying … for every prime…

Let $\mathcal G$ be a Chevalley group of adjoint type $\tau$, rank $r$, and dimension $n=r+2m$, with Lie algebra $\mathfrak g$. Let $\mathbb P[\Psi]$ be the associated…