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Algebra Seminar

An obstruction to weak approximation on some Calabi-Yau threefolds

Oct Katrina Honigs (Oregon)

Date & time: Wednesday, 14 October 2020 at 2:00PM - 3:00PM

Abstract: The study of Q-rational points on algebraic varieties is fundamental to arithmetic geometry. One of the few methods available to show that a variety does not have any Q-points is to give a Brauer-Manin obstruction. Hosono and Takagi have constructed a class of Calabi-Yau threefolds that occur as a linear section of a double quintic symmetroid and given a detailed analysis of them as complex varieties in the context of mirror symmetry. This construction can be used to produce varieties over Q as well, and these threefolds come tantalizingly equipped with a natural Brauer class. In work with Hashimoto, Lamarche and Vogt, we analyze these threefolds and their Brauer class over Q and give a condition under which the Brauer class obstructs weak approximation, though it cannot obstruct the existence of Q-rational points.

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