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Transactions of the American Mathematical Society

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The unramified Brauer group of homogeneous spaces with finite stabilizer


Author: Giancarlo Lucchini Arteche
Journal: Trans. Amer. Math. Soc. 372 (2019), 5393-5408
MSC (2010): Primary 14F22, 14M17; Secondary 14G20, 14G25
DOI: https://doi.org/10.1090/tran/7796
Published electronically: June 28, 2019
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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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Additional Information

Giancarlo Lucchini Arteche
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile
Email: luco@uchile.cl

DOI: https://doi.org/10.1090/tran/7796
Keywords: Brauer group, homogeneous spaces, finite groups, rational points
Received by editor(s): December 26, 2017
Received by editor(s) in revised form: September 25, 2018
Published electronically: June 28, 2019
Additional Notes: This work was partially supported by CONICYT via the grants “Fondecyt de Iniciación” 11170016 and “Inserción en la Academia” PAI 79170034
Article copyright: © Copyright 2019 American Mathematical Society