A descent map for curves with totally degenerate semi-stable reduction
Journal de Théorie des Nombres de Bordeaux, Tome 25 (2013) no. 1, pp. 211-244.

Soit K un corps local de caractéristique résiduelle p. Soit C une courbe sur K dont le modèle régulier propre mimimal a réduction semi-stable totalement dégénérée. Sous certaines hypothèses, nous calculons le sous-groupe rationnel de torsion première à p dans la jacobienne de C. Nous déterminons aussi la divisibilité de fibrés en droites sur C, incluant la rationalité des thêta-caractéristiques et des structures de spin supérieures. Ces calculs utilisent l’arithmétique de la fibre spéciale de C.

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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DOI : https://doi.org/10.5802/jtnb.833
@article{JTNB_2013__25_1_211_0,
     author = {Shahed Sharif},
     title = {A descent map for curves with totally degenerate semi-stable reduction},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {211--244},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {1},
     year = {2013},
     doi = {10.5802/jtnb.833},
     zbl = {1279.14026},
     mrnumber = {3063838},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.833/}
}
Shahed Sharif. A descent map for curves with totally degenerate semi-stable reduction. Journal de Théorie des Nombres de Bordeaux, Tome 25 (2013) no. 1, pp. 211-244. doi : 10.5802/jtnb.833. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.833/

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