论文标题
$ p $ - 亚种束分类的堆栈和$ p $ - adic jacquet-langlands通信
$p$-adic sheaves on classifying stacks, and the $p$-adic Jacquet-Langlands correspondence
论文作者
论文摘要
我们建立了由Scholze定义的$ P $ -ADIC JACQUET-LANGLANGLANGS函数的几个新属性，该物业是根据Lubin-Tate Tower的共同体来定义的。特别是，我们尊重Scholze的基本有限定理，证明了二元性定理，并显示了一种部分Künneth公式。使用这些结果，我们推断出Gelfand-Kirillov维度的界限，以及一些新的消失和不变结果。 我们的主要新工具是六个函数形式主义，其固体几乎是$ \ Mathcal {o}^+/p $ - 系数最近由第二作者[MAN22]开发的。本文的一个要点是扩展[MAN22]中开发的$！$ - 函子形式主义的有效性领域，以允许某些“堆栈”地图。用这种扩展形式主义的语言，我们表明，如果$ g $是一个$ p $ - ad的谎言组，则分类的小型v-stack $ b \ useverline {g} $是$ p $ - 酒精学上的平滑。
We establish several new properties of the $p$-adic Jacquet-Langlands functor defined by Scholze in terms of the cohomology of the Lubin-Tate tower. In particular, we reprove Scholze's basic finiteness theorems, prove a duality theorem, and show a kind of partial Künneth formula. Using these results, we deduce bounds on Gelfand-Kirillov dimension, together with some new vanishing and nonvanishing results. Our key new tool is the six functor formalism with solid almost $\mathcal{O}^+/p$-coefficients developed recently by the second author [Man22]. One major point of this paper is to extend the domain of validity of the $!$-functor formalism developed in [Man22] to allow certain "stacky" maps. In the language of this extended formalism, we show that if $G$ is a $p$-adic Lie group, the structure map of the classifying small v-stack $B\underline{G}$ is $p$-cohomologically smooth.
