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Motivic Zeta Functions of Abelian Varieties, and the Monodromy Conjecture by Lars Halvard Halle; Johannes Nicaise is a Mathematics article available to read on EtoBox.

What is Motivic Zeta Functions of Abelian Varieties, and the Monodromy Conjecture about?

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 in C, the value exp(2πic(A)) is an -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.

Who reads Motivic Zeta Functions of Abelian Varieties, and the Monodromy Conjecture?

Author

Lars Halvard Halle; Johannes Nicaise

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2011

Language

EN

Field

Mathematics (Physical Sciences)