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Abstract

For smooth proper schemes over a finite field k, Bilu, Ho, Srinivasan, Vogt, and Wickelgren introduced the dlog A^1-zeta function with coefficients in the Grothendieck-Witt ring of k, enriching the dlog of the classical Weil zeta function. They introduced the notion of dlog rationality, and showed this property for simple cellular schemes. In this talk, we will review their theory and show that the dlog A^1-zeta function is always rational, but not necessarily dlog rational.