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arXiv:2210.03035 [math.AG]AbstractReferencesReviewsResources

Quadratic enrichment of the logarithmic derivative of the zeta function

Margaret Bilu, Wei Ho, Padmavathi Srinivasan, Isabel Vogt, Kirsten Wickelgren

Published 2022-10-06Version 1

We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. This enrichment is related to the topology of the real points of a lift. We show a rationality result for cellular schemes over a field, and compute several examples, including toric varieties.

Comments: 38 pages
Categories: math.AG, math.AT, math.KT, math.NT
Subjects: 14G10, 14F42, 19D45, 55P25, 11G25
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