Topology of Subvarieties of Complex Semi-abelian Varieties
Topology of Subvarieties of Complex Semi-abelian Varieties
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复杂半阿贝尔簇的子簇拓扑
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
Botong Wang
中科院分区：
文献类型：
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作者：
Yongqiang Liu;L. Maxim;Botong Wang
利用Palais-Smale的非真莫尔斯理论研究了复半交换簇的光滑闭子簇及其无限循环覆盖的拓扑.作为主要的应用，我们得到了相应的积分亚历山大模的有限生成（除中次外），以及秩1局部系统在这类子簇上的符号Euler特征性质和通有消失.此外，我们给出了一个更概念性的（拓扑）解释的签署欧拉特征属性的消失诺维科夫同调。作为一个副产品，我们证明了一个通用的消失结果的$L^2$-贝蒂数非常仿射流形。我们的方法也重铸六月许的扩展Varchenko的猜想非常仿射流形，并提供了一个推广的情况下，光滑闭子品种的半阿贝尔品种的这一结果。
We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.
重新审视阿贝尔簇上反常滑轮的消失定理
DOI：
10.1007/s00029-017-0377-8
发表时间：
2018
期刊：
Selecta Mathematica
影响因子：
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作者：
Bhatt, Bhargav;Schnell, Christian;Scholze, Peter
通讯作者：
Scholze, Peter