论文标题
Hilbert of Supper的动机Zeta功能
Motivic zeta function of the Hilbert schemes of points on a surface
论文作者
论文摘要
让$ k $成为一个离散价值的字段。令$ x \ rightarrow spec k $为具有微不足道的规范捆绑包的表面。在本文中，我们在整数$ r \ subseteq k $上构建了一个方案$ hilb^n（x）$的弱Néron模型。我们利用这项构造来计算$ z_x $的$ HILB^n（x）$的动机Zeta功能。我们确定$ z_ {hilb^n（x）} $的杆子，并研究其单片属性，表明，如果单莫罗莫（Monodromy）猜想以$ x $的价格持有，则它也以$ hilb^n（x）$的速度保留。 SIT $ k $ copus cum absoluto ualore distoto。 sit $ x \ rightarrow spec k $ leuigata cum cum canonico fasce extruenti $ \ mathcal {o} _x $。在Hoc Scripto中，neroniensia paradigmata $ hilb^n（x）$ shematum super super annulo intemorum in $ k $ corpo，$ r \ r \ subset k $，constituimus。 ex hoc，functionem zetam motiuicam $ z_ {hilb^n（x）} $，dato $ z_x $，computamus。 Suos Polos Statuimus et suam monodromicam oprietatem studemus，Coniectura monodromica，Quae super $ x $ ualet，ualere super $ hilb^n（x）$ quoque demostrando。
Let $K$ be a discretely-valued field. Let $X\rightarrow Spec K$ be a surface with trivial canonical bundle. In this paper we construct a weak Néron model of the schemes $Hilb^n(X)$ over the ring of integers $R\subseteq K$. We exploit this construction in order to compute the Motivic Zeta Function of $Hilb^n(X)$ in terms of $Z_X$. We determine the poles of $Z_{Hilb^n(X)}$ and study its monodromy property, showing that if the monodromy conjecture holds for $X$ then it holds for $Hilb^n(X)$ too. Sit $K$ corpus cum absoluto ualore discreto. Sit $ X\rightarrow Spec K$ leuigata superficies cum canonico fasce congruenti $\mathcal{O}_X$. In hoc scripto defecta Neroniensia paradigmata $Hilb^n(X)$ schematum super annulo integrorum in $K$ corpo, $R \subset K$, constituimus. Ex hoc, Functionem Zetam Motiuicam $Z_{Hilb^n(X)}$, dato $Z_X$, computamus. Suos polos statuimus et suam monodromicam proprietatem studemus, coniectura monodromica, quae super $X$ ualet, ualere super $Hilb^n(X)$ quoque demostrando.
