论文标题
特征$ p $中符号变种的规范全球量化
The canonical global quantization of symplectic varieties in characteristic $p$
论文作者
论文摘要
让$ x $成为具有限制结构的特征性$ p> 2 $的字段$ k $的平滑符号变化，这是h^0（x，x，ω^1_x/d \ sathcal o_x）的类$ [η] \ class $ [η] \，其de rham差异的de rham平等形式。在本文中，我们在$（x，[η]）中构建一个函数，$ $ \ mathrm {qcoh}（x）$的Quasi-Coherent Sheaves的正式量化在$ x $上。我们还将其自然扩展构建为类别的准代捆绑包，$ \ mathrm {qcoh} _h $上的产品$ x^{（1）} \ times {\ times {\ times {\ times {\ times {\ times {\ mathbb s} $的$ x $的frobenius twist twist $ x $的frobenius twist和投射行$ {\ mathbb s} $ \ mathrm {spec} \ \！ k [h] $。它的全局部分以$ x^{（1）} \ times \ {0 \} $是$ x $上的Quasi-Coherent Sheaves的类别。如果$ x $是Aggine，则$ \ Mathrm {qCoh} _h $，仅限于$ x^{（1）} \ times \ Mathrm {spf} \ \ \！ k [[h] $，相当于$（x，[η]）$ n量化的“ frobenius-contant”量子的类别，由bezrukavnikov和kaledin定义。
Let $X$ be a smooth symplectic variety over a field $k$ of characteristic $p>2$ equipped with a restricted structure, which is a class $[η] \in H^0(X, Ω^1_X/d\mathcal O_X)$ whose de Rham differential equals the symplectic form. In this paper we construct a functorial in $(X, [η])$ formal quantization of the category $\mathrm{QCoh}(X)$ of quasi-coherent sheaves on $X$. We also construct its natural extension to a quasi-coherent sheaf of categories $\mathrm{QCoh}_h$ on the product $X^{(1)} \times {\mathbb S}$ of the Frobenius twist of $X$ and the projective line ${\mathbb S}=\mathbb P^1$, viewed as the one-point compactification of $\mathrm{Spec}\ \! k[h]$. Its global sections over $X^{(1)} \times \{0\}$ is the category of quasi-coherent sheaves on $X$. If $X$ is affine, $\mathrm{QCoh}_h$, restricted to $X^{(1)}\times \mathrm{Spf} \ \! k[[h]]$, is equivalent to the category of modules over the distinguished "Frobenius-constant" quantization of $(X,[η])$ defined by Bezrukavnikov and Kaledin.
