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How often do equations have everywhere local solutions?

Nicholas Rome, University of Michigan
Tuesday, January 17, 2023 - 11:00am to 12:00pm
MEB 243


I will discuss recent joint work with Dan Loughran and Efthymios Sofos, in which we propose a new conjecture for how many members of a family of varieties have points in all completions of Q. I will illustrate the conjecture by discussing an important new instance in which we have shown that it holds: the family of diagonal planar conics. This resolves an old problem of Serre.

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