论文标题
多项式点计数和奇怪的奇异学院在稳定曲线的模量空间上消失
Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
论文作者
论文摘要
我们以n小于或等于3的n计算m_ {4，n}上的f_q点的数量，并使用基于hasse-weil zeta函数的筛分表明它是q中的多项式。作为一种应用，我们证明，对于所有G和N，在所有奇数度小于或等于9的所有奇数中，具有n个标记点的稳定曲线的模量曲线的理性刻心共同体学组消失。这两种结果都证实了Langlands计划的预测，这是通过具有偏振的代数尖齿自动形式的指出对应关系，这些代数为1，这些代表1被分类为低重量。我们对奇数同胞的消失结果解决了1990年代Arbarello和Cornalba提出的问题。
We compute the number of F_q-points on M_{4,n}, for n less than or equal to 3, and show that it is a polynomial in q, using a sieve based on Hasse-Weil zeta functions. As an application, we prove that the rational singular cohomology groups of moduli spaces of stable curves of genus g with n marked points vanish in all odd degrees less than or equal to 9, for all g and n. Both results confirm predictions of the Langlands program, via the conjectural correspondence with polarized algebraic cuspidal automorphic representations of conductor 1, which are classified in low weight. Our vanishing result for odd cohomology resolves a problem posed by Arbarello and Cornalba in the 1990s.
