论文标题
全球Igusa Zeta功能和$ K $ - 等效
Global Igusa zeta function and $K$-equivalence
论文作者
论文摘要
令$ \ mathfrak {x} $和$ \ mathfrak {x}'$为两个平滑的投射品种，上面是$ p $ - adic field $ \ textbf {k} $的整数，通用纤维为$ x $和$ x'$。我们在$ x $和$ x'$的多元化空间上介绍了（一家）好$ s $ norms，这被称为全球Igusa Zeta在$ s $中的函数，并表明，如果$ r $ caronical-caronical Maps发送$ x $ x $ x $ x'$ x'$ birationally to Imagess分别对其图像，则在$ h^0（x）之间，$ h^0（x） rk_ {x'}）$相对于此$ s $ norm（对于$ s> 0 $和$ s \ neq 1/r $）诱导$ \ textbf {k} $的$ k $ - $ k $ - 点 - $ x $和$ x'$之间的$ \ textbf {k} $。
Let $\mathfrak{X}$ and $\mathfrak{X}'$ be two smooth projective varieties over the ring of integers of a $p$-adic field $\textbf{K}$ with generic fibers being $X$ and $X'$. We introduce a (family of) good $s$-norms on the pluricanonical spaces of $X$ and $X'$, which are called global Igusa zeta functions in $s$, and show that if the $r$-canonical maps send $X$ and $X'$ birationally to their images respectively, then any isometry between $H^0(X, rK_X)$ and $H^0(X', rK_{X'})$ with respect to this $s$-norm (for some $s > 0$ and $s \neq 1/r$) induces $K$-equivalence on the $\textbf{K}$-points between $X$ and $X'$.
