Let be a local field of residue characteristic . Let be a curve over whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- rational torsion subgroup on the Jacobian of . We also determine divisibility of line bundles on , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of .
Soit un corps local de caractéristique résiduelle . Soit une courbe sur 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 dans la jacobienne de . Nous déterminons aussi la divisibilité de fibrés en droites sur , incluant la rationalité des thêta-caractéristiques et des structures de spin supérieures. Ces calculs utilisent l’arithmétique de la fibre spéciale de .
@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/} }
TY - JOUR TI - A descent map for curves with totally degenerate semi-stable reduction JO - Journal de Théorie des Nombres de Bordeaux PY - 2013 DA - 2013/// SP - 211 EP - 244 VL - 25 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.833/ UR - https://zbmath.org/?q=an%3A1279.14026 UR - https://www.ams.org/mathscinet-getitem?mr=3063838 UR - https://doi.org/10.5802/jtnb.833 DO - 10.5802/jtnb.833 LA - en ID - JTNB_2013__25_1_211_0 ER -
Shahed Sharif. A descent map for curves with totally degenerate semi-stable reduction. Journal de Théorie des Nombres de Bordeaux, Volume 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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