4 problems

Let $S$ be a global excellent Dedekind scheme with function field $K$, and let $G$ be a smooth algebraic group over $K$. A Néron lft-model of $G$ is a smooth separated $S$-group al…

Uniform finiteness conjecture. There exists a constant $C$, depending only on $K$ and $g$, such that

Relative compactification conjecture. For some $n_0\in{\mathbf N}$, $P_{n_0}$ is a relative compactification of ${\mathcal G}$ and

Let $S$ be an excellent Dedekind scheme with function field $K$, and let $G_K$ be a smooth commutative algebraic group over $K$ that admits a regular compactification and contains…