Hasse-Witt matrices, unit roots and period integrals

An Huang Brandeis University Bong Lian Brandeis University Shing-Tung Yau Harvard University Chenglong Yu Harvard University

Number Theory mathscidoc:1802.01001

Motivated by the work of Candelas, de la Ossa and Rodriguez-Villegas [6], we study the relations between Hasse-Witt matrices and period integrals of Calabi-Yau hypersurfaces in both toric varieties and partial flag varieties. We prove a conjecture by Vlasenko [23] on higher Hasse-Witt matrices for toric hypersurfaces following Katz's method of local expansion [14, 15]. The higher Hasse-Witt matrices also have close relation with period integrals. The proof gives a way to pass from Katz's congruence relations in terms of expansion coefficients [15] to Dwork's congruence relations [8] about periods.
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  title={Hasse-Witt matrices, unit roots and period integrals},
  author={An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu},
An Huang, Bong Lian, Shing-Tung Yau, and Chenglong Yu. Hasse-Witt matrices, unit roots and period integrals. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208151459718717917.
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