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

2012/02/13 by Shahed Sharif, Sharif, Shahed
Mathematics · #11g20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11g20

paper · pdf · doi:10.48550/arxiv.1202.2891

35 pages

arxiv created 2012/02/13 · arxiv updated 2012/02/15

Abstract

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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