Hasse-Witt matrices, unit roots and period integrals
Algebraic Geometry
2018-01-08 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.1801.01189,
title = {Hasse-Witt matrices, unit roots and period integrals},
author = {An Huang and Bong Lian and Shing-Tung Yau and Chenglong Yu},
journal= {arXiv preprint arXiv:1801.01189},
year = {2018}
}
Comments
26 pages