论文标题
对称力量和动机Zeta功能的自动形态
Automorphisms of symmetric powers and motivic zeta functions
论文作者
论文摘要
我们证明，如果$ x $在特征零的字段$ k $上大于1大于1的平稳射量，以至于$ \ operatatorName {pic}（x _ {\ bar {k {k}}}）= \ mathbb {z} $ and $ x _ {\ bar {\ bar {k {k {k {k {k {k {k {k { \ operatatorName {aut}（x）\ to \ operatatorName {aut}（\ operatatorName {sym}^d（x））$是每$ d> 0 $的同构。我们还部分计算了透明表面的动机Zeta功能，并解释了粒状品种环中的Severi-Brauer品种类别之间的某些关系。
We prove that if $X$ is a smooth projective variety of dimension greater than 1 over a field $K$ of characteristic zero such that $\operatorname{Pic}(X_{\bar{K}}) = \mathbb{Z}$ and $X_{\bar{K}}$ is simply connected, then the natural map $ρ: \operatorname{Aut}(X) \to \operatorname{Aut}(\operatorname{Sym}^d(X))$ is an isomorphism for every $d > 0$. We also partially compute the motivic zeta function of a Severi-Brauer surface and explain some relations between the classes of Severi-Brauer varieties in the Grothendieck ring of varieties.
