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arXiv · 1602.04998

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

Ambrus Pal·Tomer M. Schlank
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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 weak approximation when the embedding problem has abelian kernel. As a part of our investigations we also give a new, elegant description of the Tate duality pairing and prove a new theorem on the cup product.

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Ambrus Pal, Tomer M. Schlank. 2016-02-16. The Brauer-Manin obstruction to the local-global principle for the embedding problem. https://arxiv.org/abs/1602.04998

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