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A descent map for curves with totally degenerate semi-stable reduction

Shahed Sharif — 2013

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a local field of residue characteristic $p$ . Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- $p$ rational torsion subgroup on the Jacobian of $C$ . We also determine divisibility of line bundles on $C$ , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of $C$ .

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