Motivic zeta functions of abelian varieties, and the monodromy conjecture

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

  • Lars Halvard Halle
  • Johannes Nicaise

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 Ql in C, the value exp(2πic(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 Néron model of A, which measures the behavior of the Néron model under tame base change.

OriginalsprogEngelsk
TidsskriftAdvances in Mathematics
Vol/bind227
Udgave nummer1
Sider (fra-til)610-653
Antal sider44
ISSN0001-8708
DOI
StatusUdgivet - 1 maj 2011

ID: 233909786