3 problems

Let $G$ be an additive subgroup of $\mathbb{R}^d$, and let $h(G)$ denote its Helly number. Finite subgroup Helly conjecture. For every subgroup $G\subset\mathbb{R}^d$, the Helly nu…

Let $A$ be the base ring and let $G\in\operatorname{Gr}^{+}_{A}$ be a group scheme of additive type. Write $G=\operatorname{Spec}(B_G)$ and let $\operatorname{Prim}(B_G)$ denote th…

Let $S$ be a base scheme and let $G\in\operatorname{Gr}_{S}$ be a group scheme of additive type, meaning that locally on $S$ it admits a closed embedding into $\mathbb{G}_a^N$ for…