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

Shahed Sharif^{[1]}

- [1] California State University San Marcos 333 S. Twin Oaks Valley Rd. San Marcos, CA 92096, USA

Journal de Théorie des Nombres de Bordeaux (2013)

- Volume: 25, Issue: 1, page 211-244
- ISSN: 1246-7405

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topSharif, Shahed. "A descent map for curves with totally degenerate semi-stable reduction." Journal de Théorie des Nombres de Bordeaux 25.1 (2013): 211-244. <http://eudml.org/doc/275813>.

@article{Sharif2013,

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 $C$.},

affiliation = {California State University San Marcos 333 S. Twin Oaks Valley Rd. San Marcos, CA 92096, USA},

author = {Sharif, Shahed},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {semi-stable reduction; tori over finite fields; Néron models; Picard group torsion; theta characteristic},

language = {eng},

month = {4},

number = {1},

pages = {211-244},

publisher = {Société Arithmétique de Bordeaux},

title = {A descent map for curves with totally degenerate semi-stable reduction},

url = {http://eudml.org/doc/275813},

volume = {25},

year = {2013},

}

TY - JOUR

AU - Sharif, Shahed

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

JO - Journal de Théorie des Nombres de Bordeaux

DA - 2013/4//

PB - Société Arithmétique de Bordeaux

VL - 25

IS - 1

SP - 211

EP - 244

AB - 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 $C$.

LA - eng

KW - semi-stable reduction; tori over finite fields; Néron models; Picard group torsion; theta characteristic

UR - http://eudml.org/doc/275813

ER -

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