The Néon component series of an abelian variety
Lars Halvard Halle (Universität Hannover, Germany)

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I will talk about a recent joint work with J. Nicaise, where we introduce the Néron component series of an abelian variety over a complete discretely valued field K. This is a power series in Z[[T]], which measures the number of components of the Néron model of A after tame extensions of K. I will discuss some results we have for the component series, and explain the relevance to the study of motivic zeta functions. In fact, a good description of the component series is a crucial ingredient in our proof of the motivic monodromy conjecture for abelian varieties.