zeta 函数对数导数的二次富集
Quadratic enrichment of the logarithmic derivative of the zeta function
AI总结：
本文将有限域上代数簇的 zeta 函数对数导数富集到 Grothendieck–Witt 群系数的幂级数，证明其与实点拓扑的联系，并对胞腔概形建立有理性结果，验证其为母题测度。
摘要：
我们将有限域上代数簇的 zeta 函数的对数导数富集为系数取值于 Grothendieck–Witt 群的幂级数。我们证明这种富集与某个提升的实点拓扑相关。对于域上的胞腔概形，我们证明了该 zeta 函数的富集对数导数的一个有理性结果，作为 Weil 猜想一部分的类比。我们还计算了若干例子，包括环面簇，并证明该富集是一个母题测度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
