Motivic zeta functions of abelian varieties, and the monodromy conjecture
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Motivic zeta functions of abelian varieties, and the monodromy conjecture. / Halle, Lars Halvard; Nicaise, Johannes.
I: Advances in Mathematics, Bind 227, Nr. 1, 01.05.2011, s. 610-653.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Motivic zeta functions of abelian varieties, and the monodromy conjecture
AU - Halle, Lars Halvard
AU - Nicaise, Johannes
PY - 2011/5/1
Y1 - 2011/5/1
N2 - 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.
AB - 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.
KW - Abelian varieties
KW - Monodromy conjecture
KW - Motivic zeta functions
KW - Néron models
UR - http://www.scopus.com/inward/record.url?scp=79952706904&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2011.02.011
DO - 10.1016/j.aim.2011.02.011
M3 - Journal article
AN - SCOPUS:79952706904
VL - 227
SP - 610
EP - 653
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 1
ER -
ID: 233909786