The Brauer group of torsors and its arithmetic applications

David Harari[1]; Alexei N. Skorobogatov[2]

  • [1] École Normale Supérieure, DMA, 45 rue d'Ulm, 75230 Paris Cedex 05 (France)
  • [2] Imperial College, Department of Mathematics, 180 Queen's Gate, London SW7 2BZ (Royaume-Uni)

Annales de l'Institut Fourier (2003)

  • Volume: 53, Issue: 7, page 1987-2019
  • ISSN: 0373-0956

Abstract

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Let X be an algebraic variety defined over a field k of characteristic 0 , and let Y be an X -torsor under a torus. We compute the Brauer group of Y . In the case of a number field k we deduce results concerning the arithmetic of X .

How to cite

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Harari, David, and Skorobogatov, Alexei N.. "The Brauer group of torsors and its arithmetic applications." Annales de l'Institut Fourier 53.7 (2003): 1987-2019. <http://eudml.org/doc/116091>.

@article{Harari2003,
abstract = {Let $X$ be an algebraic variety defined over a field $k$ of characteristic $0$, and let $Y$ be an $X$-torsor under a torus. We compute the Brauer group of $Y$. In the case of a number field $k$ we deduce results concerning the arithmetic of $X$.},
affiliation = {École Normale Supérieure, DMA, 45 rue d'Ulm, 75230 Paris Cedex 05 (France); Imperial College, Department of Mathematics, 180 Queen's Gate, London SW7 2BZ (Royaume-Uni)},
author = {Harari, David, Skorobogatov, Alexei N.},
journal = {Annales de l'Institut Fourier},
keywords = {Brauer group; Hasse principle; universal torsor},
language = {eng},
number = {7},
pages = {1987-2019},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Brauer group of torsors and its arithmetic applications},
url = {http://eudml.org/doc/116091},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Harari, David
AU - Skorobogatov, Alexei N.
TI - The Brauer group of torsors and its arithmetic applications
JO - Annales de l'Institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 7
SP - 1987
EP - 2019
AB - Let $X$ be an algebraic variety defined over a field $k$ of characteristic $0$, and let $Y$ be an $X$-torsor under a torus. We compute the Brauer group of $Y$. In the case of a number field $k$ we deduce results concerning the arithmetic of $X$.
LA - eng
KW - Brauer group; Hasse principle; universal torsor
UR - http://eudml.org/doc/116091
ER -

References

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