Multiplicative zeta function and logarithmic point counting over finite fields
K-Theory and Homology
2017-05-04 v1 Algebraic Geometry
Abstract
The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function, which instead respects the tensor product of motives. There is no analogue of the Weil conjectures, and we give a sufficient criterion for an analytic continuation to exist. This happens, for example, for cellular varieties, abelian varieties, or genus g > 1 curves with a supersingular Jacobian.
Cite
@article{arxiv.1705.01192,
title = {Multiplicative zeta function and logarithmic point counting over finite fields},
author = {Oliver Braunling},
journal= {arXiv preprint arXiv:1705.01192},
year = {2017}
}