

Iskovskikh Seminar
March 24, 2011 18:00, Moscow, Steklov Mathematical Institute, room 540






The unramified Brauer group of quotients by algebraic groups
A. L. Fomin^{} ^{} Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
The report is based on ColliotThelene's and Sansuc's papers.
Two theorems will be proved. The ground field is the field of complex numbers.
1. Let $G$ be a connected algebraic group and let $V$ be an almost free linear
representation of $G$. Then the unramified Brauer group of the field of
rational functions on $V/G$ is trivial.
2. Let $G$ be a connected simply connected algebraic group
and let $H$ be its connected closed subgroup. Then the unramified Brauer group of $G/H$ is trivial.

