4 problems

Fix a number field $F$. For each positive integer $N$, let $r_F(N)$ be the maximum of $\operatorname{Rank}_{\mathbb{Z}}E(F)$ over elliptic curves $E/F$ whose conductor…

Let $K(C)$ be the function field of a curve $C$ over a number field $K$, with genus $g$, and let ${\mathcal E}/K(C)$ be a non-constant elliptic curve, meaning…

Consider the six tensor-network representations in Table: TT-rank over $\mathbb{R}$, TT-rank over $\mathbb{R}_{\geq 0}$, Born-rank over $\mathbb{R}$, Born-rank over $\mathbb{C}$, p…

Let $\mathcal{S}$ be a non-reflexive $n$-dimensional space of operators over a field $\mathbb{K}$ with sufficiently large cardinality. The preceding result gives a non-zero operato…