Motivic zeta functions of abelian varieties, and the monodromy conjecture

作者：Halle Lars Halvard; Nicaise Johannes^*

来源：Advances in Mathematics, 2011, 227(1): 610-653.

DOI：10.1016/j.aim.2011.02.011

• Motivic zeta functions
• Monodromy conjecture
• Abelian varieties
• Neron models

We prove for abelian varieties a global form of Denef and Loeser's motivic monodromy conjecture, in arbitrary characteristic. More precisely, we prove that for every tamely ramified abelian variety A over a complete discretely valued field with algebraically closed residue field, its motivic zeta function has a unique pole at Chai's base change conductor c(A) of A, and that the order of this pole equals one plus the potential toric rank of A. Moreover, we show that for every embedding of Q(l) in C, the value exp(2 pi ic(A)) is an l-adic tame monodromy eigenvalue of A. The main tool in the paper is Edixhoven's filtration on the special fiber of the Neron model of A, which measures the behavior of the Neron model under tame base change.

• 出版日期2011-5-1
• 单位KU Leuven