HasseWitt matrices, unit roots and period integrals
Abstract
Motivated by the work of Candelas, de la Ossa and RodriguezVillegas [6], we study the relations between HasseWitt matrices and period integrals of CalabiYau hypersurfaces in both toric varieties and partial flag varieties. We prove a conjecture by Vlasenko [23] on higher HasseWitt matrices for toric hypersurfaces following Katz's method of local expansion [14, 15]. The higher HasseWitt 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1801.01189
 arXiv:
 arXiv:1801.01189
 Bibcode:
 2018arXiv180101189H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G10;
 32G20
 EPrint:
 26 pages