Counting rational points on stacks


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February 5, 2020 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Jordan Ellenberg - University of Wisconsin at Madison

There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of a new definition of height for rational points on (certain) stacks over global fields. I talked about some aspects of this work at Barry’s birthday conference, and will try in this talk to emphasize different points, including a conjecture about the asymptotic counting function for points of bounded height on a stack X which simultaneously generalizes the Manin conjectures (the case where X is a variety) and the Malle conjectures (the case where X is a classifying stack BG.)