### Abstract

We study the subgroup B _{0}(G) of H ^{2}(G, ℚ/ℤ) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B _{0}(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B _{0}(G) is trivial for finite simple groups of Lie type A _{ℓ}.

Original language | English (US) |
---|---|

Pages (from-to) | 935-949 |

Number of pages | 15 |

Journal | American Journal of Mathematics |

Volume | 126 |

Issue number | 4 |

State | Published - Aug 2004 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*American Journal of Mathematics*,

*126*(4), 935-949.

**Unramified brauer groups of finite simple groups of lie type A ℓ .** / Bogomolov, Fedor; Maciel, Jorge; Petrov, Tihomir.

Research output: Contribution to journal › Article

*American Journal of Mathematics*, vol. 126, no. 4, pp. 935-949.

}

TY - JOUR

T1 - Unramified brauer groups of finite simple groups of lie type A ℓ

AU - Bogomolov, Fedor

AU - Maciel, Jorge

AU - Petrov, Tihomir

PY - 2004/8

Y1 - 2004/8

N2 - We study the subgroup B 0(G) of H 2(G, ℚ/ℤ) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B 0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B 0(G) is trivial for finite simple groups of Lie type A ℓ.

AB - We study the subgroup B 0(G) of H 2(G, ℚ/ℤ) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B 0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B 0(G) is trivial for finite simple groups of Lie type A ℓ.

UR - http://www.scopus.com/inward/record.url?scp=4043119799&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4043119799&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4043119799

VL - 126

SP - 935

EP - 949

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 4

ER -