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.
Halle, L.H., Nicaise, J. (2011). JUMPS AND MONODROMY OF ABELIAN VARIETIES. DOCUMENTA MATHEMATICA, 16, 937-968.
JUMPS AND MONODROMY OF ABELIAN VARIETIES
Halle, Lars Halvard;
2011
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 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.File in questo prodotto:
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