Motivic zeta functions of degenerating Calabi-Yau varieties

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Title: Motivic zeta functions of degenerating Calabi-Yau varieties
Authors: Halle, LH
Nicaise, J
Item Type: Journal Article
Abstract: We study motivic zeta functions of degenerating families of Calabi-Yau varieties. Our main result says that they satisfy an analog of Igusa's monodromy conjecture if the family has a so-called Galois-equivariant Kulikov model; we provide several classes of examples where this condition is verified. We also establish a close relation between the zeta function and the skeleton that appeared in Kontsevich and Soibelman's non-archimedean interpretation of the SYZ conjecture in mirror symmetry.
Issue Date: 10-Aug-2017
Date of Acceptance: 31-Jul-2017
URI: http://hdl.handle.net/10044/1/52210
DOI: https://dx.doi.org/10.1007/s00208-017-1578-3
ISSN: 0025-5831
Publisher: Springer Verlag
Start Page: 1277
End Page: 1320
Journal / Book Title: Mathematische Annalen
Volume: 370
Issue: 3-4
Copyright Statement: © Springer-Verlag GmbH Deutschland 2017. The final publication is available at Springer via http://dx.doi.org/10.1007/s00208-017-1578-3
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 306610
Keywords: Science & Technology
Physical Sciences
Mathematics
ARCHIMEDEAN ANALYTIC SPACES
ABELIAN-VARIETIES
NERON MODELS
TAME RAMIFICATION
STABLE REDUCTION
ETALE COHOMOLOGY
RIGID VARIETIES
MAXIMAL ORDER
TRACE FORMULA
K3 SURFACES
math.AG
0101 Pure Mathematics
General Mathematics
Notes: New result on existence of Kulikov models for abelian varieties added in section 5.1
Publication Status: Published
Online Publication Date: 2017-08-10
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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