Uniform bounds for the number of rational points on curves of small Mordell--Weil rank

Eric Katz, Joseph Rabinoff, David Zureick-Brown

Let $X$ be a curve of genus $g\ge 2$ over a number field $F$ of degree $d=[F:Q]$. The conjectural existence of a uniform bound $N(g,d)$ on the number $\#X(F)$ of $F$-rational po…