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

Abstract

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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 .

How to cite

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Sharif, 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 -

References

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