The Chabauty-Coleman bound at a prime of bad reduction and clifford bounds for geometric rank functions

Eric Katz, David Zureick-Brown

Let X be a curve over a number field K with genus g>=2, $\pp$ a prime of O_K over an unramified rational prime p>2r, J the Jacobian of X, r=rank J(K), and $\scrX$ a regular proper…