Brauer-Manin obstruction to the local-global principle for the embedding problem

Ambrus Pál; Tomer M. Schlank

doi:10.1142/S1793042122500786

Brauer-Manin obstruction to the local-global principle for the embedding problem

Ambrus Pál^*
, Tomer M. Schlank

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic) Brauer-Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel.

Original language	English
Pages (from-to)	1535-1565
Number of pages	31
Journal	International Journal of Number Theory
Volume	18
Issue number	7
DOIs	https://doi.org/10.1142/S1793042122500786
State	Published - 1 Aug 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.

Keywords

Brauer-Manin obstruction
Embedding problems
local-global principle

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10.1142/S1793042122500786

Cite this

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abstract = "We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic) Brauer-Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel.",

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AB - We study an analogue of the Brauer-Manin obstruction to the local-global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic) Brauer-Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel.

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KW - Embedding problems

KW - local-global principle

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Brauer-Manin obstruction to the local-global principle for the embedding problem

Abstract

Bibliographical note

Keywords

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