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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von L. H. Halle

Behaviour of component groups of Neron models under ramified extensions

Let A be an abelian variety defined over a complete discretely valued field K, and let N(A) denote the associated Neron model of A. The component group G(A) parametrizes the connected components of the special fiber of N(A). I will discuss how the component group changes under ramified extensions of K, and how knowledge of this behaviour gives information about the motivic zeta function of A.

This is joint work with Johannes Nicaise.