HITCHIN FIBRATIONS, ABELIAN SURFACES, AND THE P=W CONJECTURE
HITCHIN FIBRATIONS, ABELIAN SURFACES, AND THE P=W CONJECTURE
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DOI：
10.1090/jams/989
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发表时间：
2021-11-02
影响因子：
3.9
通讯作者：
Shen, Junliang
中科院分区：
文献类型：
--
作者：
de Cataldo, Mark Andrea;Maulik, Davesh;Shen, Junliang
我们通过阿贝尔曲面研究希钦纤维的拓扑结构。我们建立了亏格曲线和任意等级的 P= W 猜想。在更高的属和任意等级中，我们证明 P= W 对于由同义反复类生成的上同调子代数成立。此外，我们证明所有同义反复生成器都位于反常过滤的正确部分，正如 P= W 猜想所预测的那样。结合梅利特最近的工作，这减少了对反常过滤的多重性的完整猜想。
We study the topology of Hitchin fibrations via abelian surfaces. We establish the P= W conjecture for genuscurves and arbitrary rank. In higher genus and arbitrary rank, we prove that P= W holds for the subalgebra of cohomology generated by even tautological classes. Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted by the P= W conjecture. In combination with recent work of Mellit, this reduces the full conjecture to the multiplicativity of the perverse filtration.