Invertible Calabi-Yau Orbifolds over Finite Fields

2025/04/23 by Marco Aldi, Aldi, Marco, Andrija Peruničić +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.16716

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

In the context of Berglund-Huebsch mirror symmetry, we compute the eigenvalues of the Frobenius endomorphism acting on a p-adic version of Borisov's complex. As a result, we conjecture an explicit formula for the number of points of crepant resolutions of invertible Calabi-Yau orbifolds defined over a finite field.

Citations

• Zeta functions of alternate mirror Calabi-Yau families
• Strong arithmetic mirror symmetry and toric isogenies
• LG/CY correspondence: the state space isomorphism
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring"
• The Zeta-Function of a p-Adic Manifold, Dwork Theory for Physicists
• Frobenius action on l-adic Chen-Ruan cohomology
• Mirror Symmetry For Zeta Functions
• The Mirror Map for Invertible LG Models
• On the Classification of Quasihomogeneous Functions
• A generalized construction of mirror manifolds
• Numbers of solutions of equations in finite fields

Related

• The Crepant Resolution Conjecture
• Landau-Ginzburg Mirror Symmetry for Orbifolded Frobenius Algebras
• Singularities with Symmetries, orbifold Frobenius algebras and Mirror Symmetry
• Comparison of non-archimedean and logarithmic mirror constructions via the Frobenius structure theorem
• The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus