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

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If you have a question about this talk, please contact Tom Fisher .

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 Brauer-Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel and show that the analogue of the algebraic Brauer-Manin obstruction is equivalent to the analogue of the abelian descent obstruction. In the course of our investigations we give a new, elegant description of the Tate duality pairing and prove a new theorem on the cup product in group cohomology. (Joint work with Tomer Schlank.)

This talk is part of the Number Theory Seminar series.

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Wolfson Hall, Churchill College, Cambridge, CB3 0DS Rooms SG1 & SG2, Alison Richard Building, 7 West Road, Cambridge, CB3 9DT Physics and Chemistry of Solids Group

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