The unramified Brauer group of homogeneous spaces with finite stabilizer

Lucchini Arteche, Giancarlo

doi:10.1090/tran/7796

The unramified Brauer group of homogeneous spaces with finite stabilizer
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Trans. Amer. Math. Soc. 372 (2019), 5393-5408 Request permission

Abstract:

We give formulas for calculating the unramified Brauer group of a homogeneous space $X$ of a semisimple simply connected group $G$ with finite geometric stabilizer $\bar F$ over a wide family of fields of characteristic $0$. When $k$ is a number field, we use these formulas in order to study the Brauer–Manin obstruction to the Hasse principle and weak approximation. We prove in particular that the Brauer-Manin pairing is constant on $X(k_v)$ for every $v$ outside of an explicit finite set of nonarchimedean places of $k$.

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