## Abstract

Let K be a field and Br(K) its Brauer group. If L/K is a field extension, then the relative Brauer group Br(L/K) is the kernel of the restriction map res_{L/K}: Br(K) → Br(L). A subgroup of Br(K) is called an algebraic relative Brauer group if it is of the form Br(L/K) for some algebraic extension L/K. In this paper, we consider the m-torsion subgroup Br_{m}(K) consisting of the elements of Br(K) killed by m, where m is a positive integer, and ask whether it is an algebraic relative Brauer group. The case K = ℚ is already interesting: the answer is yes for m squarefree, and we do not know the answer for m arbitrary. A counterexample is given with a two-dimensional local field K = k((t)) and m = 2.

Original language | English |
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Pages (from-to) | 1333-1337 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 5 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |