论文标题
$ A_G $的最重要的合理共同体
On the Top-Weight Rational Cohomology of $A_g$
论文作者
论文摘要
我们计算出$ g = 5 $，$ 6 $和$ 7 $的$ a_g $的顶级重量理性共同体，我们给出了$ A_8，A_9，$和$ A_ {10} $的顶级重量理性共同体的消失结果。当$ g = 5 $和$ g = 7 $时，我们在奇数上展示了$ a_g $的非零同胞组，从而回答了格鲁什夫斯基突出显示的问题。我们的方法发展了$ a_g $的顶级重量共同体与主要两极分化的热带阿伯利亚品种等级$ g $的链接的同源性之间的关系。为了计算后者，我们使用Elbaz-Vincent-Gangl-Soulé使用的Voronoi综合体。我们的计算为$ a_g $ 0 $ 0 $ $ a_g $ 0 $的紧凑型共同体学课提供了自然候选人，这些$ $ 0 $，在吉赛因光谱序列下为后者空间制作了$ a_g $ in Regize $ 0 $的稳定的共同体学课。
We compute the top-weight rational cohomology of $A_g$ for $g=5$, $6$, and $7$, and we give some vanishing results for the top-weight rational cohomology of $A_8, A_9,$ and $ A_{10}$. When $g=5$ and $g=7$, we exhibit nonzero cohomology groups of $A_g$ in odd degree, thus answering a question highlighted by Grushevsky. Our methods develop the relationship between the top-weight cohomology of $A_g$ and the homology of the link of the moduli space of principally polarized tropical abelian varieties of rank $g$. To compute the latter we use the Voronoi complexes used by Elbaz-Vincent-Gangl-Soulé. Our computations give natural candidates for compactly supported cohomology classes of $A_g$ in weight $0$ that produce the stable cohomology classes of the Satake compactification of $A_g$ in weight $0$, under the Gysin spectral sequence for the latter space.
