Jumps and monodromy of abelian varieties

2010/09/20 by Lars Halvard Halle, Johannes Nicaise, Halle, Lars Halvard +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1009.3777

openalex publication_date 2010/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a strong form of the motivic monodromy conjecture for abelian varieties, by showing that the order of the unique pole of the motivic zeta function is equal to the size of the maximal Jordan block of the corresponding monodromy eigenvalue. Moreover, we give a Hodge-theoretic interpretation of the fundamental invariants appearing in the proof.

Related

• Motivic zeta functions of abelian varieties, and the monodromy conjecture
• Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
• Monodromy conjecture for semi-quasihomogeneous hypersurfaces
• The local motivic monodromy conjecture for simplicial nondegenerate singularities
• Introduction to the monodromy conjecture