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- Title
Hasse–Witt matrices, unit roots and period integrals.
- Authors
Huang, An; Lian, Bong; Yau, Shing-Tung; Yu, Chenglong
- Abstract
Motivated by the work of Candelas et al. (Calabi–Yau manifolds over finite fields, I. arXiv:hep-th/0012233, 2000) on counting points for quintic family over finite fields, we study the relations among Hasse–Witt matrices, unit-root part of zeta functions and period integrals of Calabi–Yau hypersurfaces in both toric varieties and flag varieties. We prove a conjecture by Vlasenko (Higher Hasse–Witt matrices. Indag Math 29(5):1411–1424, 2018) on unit-root F-crystals for toric hypersurfaces following Katz's local expansion method (1984, 1985) in logarithmic setting. The Frobenius matrices of unit-root F-crystals also have close relation with period integrals. The proof gives a way to pass from Katz's congruence relations in terms of expansion coefficients (1985) to Dwork's congruence relations (1969) about periods.
- Subjects
CONGRUENCE lattices; FINITE fields; CALABI-Yau manifolds; ZETA functions; INTEGRAL functions; QUINTIC equations; TORIC varieties
- Publication
Mathematische Annalen, 2023, Vol 387, Issue 1/2, p145
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-022-02464-y