Geodesic
Jumps and monodromy of abelian varieties
Documenta mathematica, Tome 16 (2011), pp. 937-968
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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.
DOI : 10.4171/dm/357
Classification : 11G10, 14D05, 14D07 
@article{10_4171_dm_357,
     author = {Lars Halvard Halle and Johannes Nicaise},
     title = {Jumps and monodromy of abelian varieties},
     journal = {Documenta mathematica},
     pages = {937--968},
     year = {2011},
     volume = {16},
     doi = {10.4171/dm/357},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/357/}
}
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Lars Halvard Halle; Johannes Nicaise. Jumps and monodromy of abelian varieties. Documenta mathematica, Tome 16 (2011), pp. 937-968. doi: 10.4171/dm/357

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