3 problems

Nontrivial-unit conjecture. If $\deg g>\deg h$ and $h\ne 0$, then

Let $K$ be a non-big field, meaning an algebraic extension of $\mathbb{Q}$ that is not big, and let $R_K$ denote the ring constructed from the unit group of $K$. Triviality conject…

Shapes of unit lattices conjectures. The closure $\overline{\Omega}$ in the modular surface is non-compact, the closure $\overline{\Omega}$ in the modular surface has non-empty int…