Hasse-Witt matrices, unit roots and period integrals

2018/01/03 by An Huang, Bong Lian, Huang, An +5
Mathematics · #14G10 #32G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14G10 #msc:32G20

paper · pdf · doi:10.48550/arxiv.1801.01189

26 pages

arxiv created 2018/01/03 · arxiv updated 2018/01/08

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.

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