Jumps and Monodromy of Abelian Varieties

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 maximal rank of a Jordan block of the corresponding monodromy eigenvalue. Moreover, we give a Hodge-theoretic interpretation of the fundamental invariants appearing in the proof.

2010 Mathematics Subject Classification: MSC2000: 11G10, 14D05, 14D07

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