Geodesic
Motivic zeta functions of the Hilbert schemes of points on a surface
Documenta mathematica, Tome 29 (2024) no. 4, pp. 763-804

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Let K be a discretely-valued field. Let X→SpecK be a surface with trivial canonical bundle. In this paper we construct a weak Néron model of the schemes Hilbn(X) over the ring of integers R⊆K. We exploit this construction in order to compute the motivic zeta function of Hilbn(X) in terms of the motivic zeta functions of X and of its base-changes with respect to the totally ramified extensions of K. We determine the poles of ZHilbn(X)​ and study its monodromy property, showing that if the monodromy conjecture holds for X then it holds for Hilbn(X) too.
DOI : 10.4171/dm/948
Classification : 14G10, 14J42, 14C05
Mots-clés : motivic integration, motivic zeta functions, monodromy conjecture, Hilbert schemes 
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     author = {Luigi Pagano},
     title = {Motivic zeta functions of the {Hilbert} schemes of points on a surface},
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Luigi Pagano. Motivic zeta functions of the Hilbert schemes of points on a surface. Documenta mathematica, Tome 29 (2024) no. 4, pp. 763-804. doi: 10.4171/dm/948

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