Lifting Divisors on a Generic Chain of Loops

Abstract Let $C$ be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on $C$ , confirming a conjecture of Cools, Draisma, Robeva, and the third author.

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