论文标题
Zeta功能的对数衍生物的二次富集
Quadratic enrichment of the logarithmic derivative of the zeta function
论文作者
论文摘要
我们定义了一个在有限场上的Zeta功能的对数衍生物的富集，以在Grothendieck-Witt组中具有系数的功率序列。我们表明，这种丰富与升降机的真实点的拓扑有关。对于一个领域的细胞方案，我们证明了Zeta功能的这种富集对数衍生物的合理性结果，作为Weil猜想的一部分的类似物。我们还计算了几个示例，包括曲折品种，并表明富集是一种动机措施。
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. We show that this enrichment is related to the topology of the real points of a lift. For cellular schemes over a field, we prove a rationality result for this enriched logarithmic derivative of the zeta function as an analogue of part of the Weil conjectures. We also compute several examples, including toric varieties, and show that the enrichment is a motivic measure.
