论文标题
$ \ mathbb z_ \ ell $ - 和$ \ mathbb q_ \ ell $ -sheaves in Diamonds上的6个功能形式主义
The 6-Functor Formalism for $\mathbb Z_\ell$- and $\mathbb Q_\ell$-Sheaves on Diamonds
论文作者
论文摘要
对于每个核$ \ MATHBB Z_ \ ELL $ -ALGEBRA $λ$和每个小型V-stack $ X $，我们构建$ \ infty $ -CAGETORY $ \ MATHCAL D _ {\ MATHRM {nucrm {nucrm {nuc}}（X，X，λ）$ nucial $ unip $λ$ -Modules on $ x $。然后，我们为这些滑轮构建了一个完整的6函数形式主义，以$λ= \ Mathbb f_ \ ell $概括了典型的6个函数形式主义。 $λ$的突出选择是$ \ mathbb z_ \ ell $，$ \ mathbb q_ \ ell $和$ \ bar {\ mathbb q_ \ ell} $，尤其是在后两种情况下，在以前没有找到满意的6个函数形式主义。应用于分类的堆栈，我们获得了核代表理论，即在Banach空间过滤的colimits上连续表示。
For every nuclear $\mathbb Z_\ell$-algebra $Λ$ and every small v-stack $X$ we construct an $\infty$-category $\mathcal D_{\mathrm{nuc}}(X,Λ)$ of nuclear $Λ$-modules on $X$. We then construct a full 6-functor formalism for these sheaves, generalizing the étale 6-functor formalism for $Λ= \mathbb F_\ell$. Prominent choices for $Λ$ are $\mathbb Z_\ell$, $\mathbb Q_\ell$ and $\bar{\mathbb Q_\ell}$ and especially in the latter two cases, no satisfying 6-functor formalism has been found before. Applied to classifying stacks we obtain a theory of nuclear representations, i.e. continuous representations on filtered colimits of Banach spaces.
