Insufficiency of the Brauer-Manin obstruction for Enriques surfaces

Jen Berg (UT Austin)

Let X be a smooth projective variety over a global field k. In 1970, Manin showed the the Brauer group of X could obstruct the existence of k-rational points. In this talk, we discuss results that show that the Brauer-Manin obstruction is insufficient to explain all failures of the Hasse principle for Enriques surfaces. This extends work of Varilly-Alvarado and Viray from 2011, in which the authors constructed an Enriques surface X over the rationals with an etale-Brauer obstruction to the Hasse principle, but no algebraic Brauer-Manin obstruction. This is joint work with F. Balestrieri, M. Manes, J. Park, and B. Viray.

Tuesday, April 7th, at 4:00pm in HBH 227

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