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Generic vanishing for semi-abelian varieties and integral Alexander modules

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Abstract

We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological applications. In particular, we obtain finiteness properties for the integral Alexander modules of complex algebraic varieties mapping to semi-abelian varieties. Similar results were recently derived by the authors by using Morse-theoretic arguments.

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Acknowledgements

We are grateful to Zhixian Zhu for useful discussions. The authors thank the Mathematics Departments at East China Normal University (Shanghai, China) and University of Science and Technology of China (Hefei, China) for hospitality during the preparation of this work. The first author is partially supported by Nero Budur’s research project G0B2115N from the Research Foundation of Flanders. The second author is partially supported by the Simons Foundation Collaboration Grant #567077 and by the Romanian Ministry of National Education, CNCS-UEFISCDI, grant PN-III-P4-ID-PCE-2016-0030. The third author is partially supported by NSF grant DMS-1701305.

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Liu, Y., Maxim, L. & Wang, B. Generic vanishing for semi-abelian varieties and integral Alexander modules. Math. Z. 293, 629–645 (2019). https://doi.org/10.1007/s00209-018-2194-y

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