Abstract
We prove a 1999 conjecture of Veys, which says that the opposite of the log-canonical threshold is the only possible pole of maximal order of Denef and Loeser’s motivic zeta function associated with a germ of a regular function on a smooth variety over a field of characteristic . We apply similar methods to study the weight function on the Berkovich skeleton associated with a degeneration of Calabi–Yau varieties. Our results suggest that the weight function induces a flow on the nonarchimedean analytification of the degeneration towards the Kontsevich–Soibelman skeleton.
Citation
Johannes Nicaise. Chenyang Xu. "Poles of maximal order of motivic zeta functions." Duke Math. J. 165 (2) 217 - 243, 1 February 2016. https://doi.org/10.1215/00127094-3165648
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