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arXiv · 1705.01192

Multiplicative zeta function and logarithmic point counting over finite fields

Oliver Braunling
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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.

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Oliver Braunling. 2017-05-02. Multiplicative zeta function and logarithmic point counting over finite fields. https://arxiv.org/abs/1705.01192

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