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The Chabauty–Coleman bound at a prime of bad reduction and Clifford bounds for geometric rank functions
Abstract Let $X$ be a curve over a number field $K$ with genus $g\geq 2$ , $\mathfrak{p}$ a prime of ${ \mathcal{O} }_{K} $ over an unramified rational prime $p\gt 2r$ , $J$ the Jacobian of $X$ , $r= \mathrm{rank} \hspace{0.167em} J(K)$ , and $\mathscr{X}$ a regular proper model of …