The period-index problem in WC-groups IV: a local transition theorem

Pete L. Clark[1]

  • [1] Department of Mathematics Boyd Graduate Studies Research Center University of Georgia Athens, GA 30602-7403, USA

Journal de Théorie des Nombres de Bordeaux (2010)

  • Volume: 22, Issue: 3, page 583-606
  • ISSN: 1246-7405

Abstract

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Let K be a complete discretely valued field with perfect residue field k . Assuming upper bounds on the relation between period and index for WC-groups over k , we deduce corresponding upper bounds on the relation between period and index for WC-groups over K . Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and a generalization of the period-index obstruction map to flat cohomology. In an appendix, we consider some related issues of a field-arithmetic nature.

How to cite

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Clark, Pete L.. "The period-index problem in WC-groups IV: a local transition theorem." Journal de Théorie des Nombres de Bordeaux 22.3 (2010): 583-606. <http://eudml.org/doc/116422>.

@article{Clark2010,
abstract = {Let $K$ be a complete discretely valued field with perfect residue field $k$. Assuming upper bounds on the relation between period and index for WC-groups over $k$, we deduce corresponding upper bounds on the relation between period and index for WC-groups over $K$. Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and a generalization of the period-index obstruction map to flat cohomology. In an appendix, we consider some related issues of a field-arithmetic nature.},
affiliation = {Department of Mathematics Boyd Graduate Studies Research Center University of Georgia Athens, GA 30602-7403, USA},
author = {Clark, Pete L.},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {3},
pages = {583-606},
publisher = {Université Bordeaux 1},
title = {The period-index problem in WC-groups IV: a local transition theorem},
url = {http://eudml.org/doc/116422},
volume = {22},
year = {2010},
}

TY - JOUR
AU - Clark, Pete L.
TI - The period-index problem in WC-groups IV: a local transition theorem
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2010
PB - Université Bordeaux 1
VL - 22
IS - 3
SP - 583
EP - 606
AB - Let $K$ be a complete discretely valued field with perfect residue field $k$. Assuming upper bounds on the relation between period and index for WC-groups over $k$, we deduce corresponding upper bounds on the relation between period and index for WC-groups over $K$. Up to a constant depending only on the dimension of the torsor, we recover theorems of Lichtenbaum and Milne in a “duality free” context. Our techniques include the use of LLR models of torsors under abelian varieties with good reduction and a generalization of the period-index obstruction map to flat cohomology. In an appendix, we consider some related issues of a field-arithmetic nature.
LA - eng
UR - http://eudml.org/doc/116422
ER -

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