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Igusa Zeta Functions and the Non-archimedean SYZ Fibration

We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimede...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2018-03, Vol.43 (1), p.31-44
Main Author: Nicaise, Johannes
Format: Article
Language:English
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Summary:We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimedean geometry and mirror symmetry; we will outline these relations at the end of the paper. This text is intended to be a low-tech introduction to these topics; we only assume that the reader has a basic knowledge of algebraic geometry.
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-017-0241-0