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Zeta statistics

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Margaret Bilu
IST Austria
Tue, 2021-07-20 14:00 - 15:30

Many questions in number theory have a natural analogue, of more geometric nature, formulated in the Grothendieck ring of varieties. For example, Poonen's finite field Bertini theorem has a motivic counterpart due to Vakil and Wood; however, despite the clear similarities between these two results, none of the two can be deduced from the other. The aim of this talk is to describe and motivate a conjectural way of comparing such statements in arithmetic and motivic statistics, by reformulating them in terms of the convergence of zeta functions in different topologies. We will finish by mentioning some concrete settings where our conjectures are satisfied. This is joint work with Ronno Das and Sean Howe.



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