论文标题
$ Q $ -Crystals和$ Q $ -Connections
$q$-crystals and $q$-connections
论文作者
论文摘要
我们研究$ q $ - 连接的类别如何取决于坐标的选择。我们利用Bhatt和Scholze的$ Q $ -CRYSTALLINE网站，该网站基于$ Q $ -PD结构的坐标配方，以便将$ Q $ -Crystals和$ Q $ -Connections与$ P $ -ADIC环境相关联。这在$ p $ - adiC设置中的不同选择的$ q $连接类别之间产生了自然等效性。可以用差分运算符明确描述等效性。为了获得全球等效性，我们修补了$ p $ - 亚种差分运算符以创建全局。该过程并非完全正式，我们只能在倒置2美元后获得全球等价。
We study how the category of $q$-connections depends on the choice of coordinates. We exploit Bhatt's and Scholze's $q$-crystalline site, which is based on a coordinate free formulation of $q$-PD structures, in order to relate $q$-crystals and $q$-connections in the $p$-adic setting. This yields a natural equivalence between the the categories of $q$-connections for different choices of coordinates in the $p$-adic setting. The equivalence can be described explicitly in terms of differential operators. In order to obtain a global equivalence, we patch the $p$-adic differential operators to create a global one. The process is not entirely formal, and we are only able to obtain a global equivalence after inverting $2$.
