论文标题
P-Adic Simpson Correponcence通过棱柱形晶体
P-adic Simpson correpondence via prismatic crystals
论文作者
论文摘要
让$ \ frakx $成为$ \ calo_k $的平滑$ p $ -ADIC正式方案，带有ADIC通用光纤$ x $。我们获得了类别$ \ vect（（（\ frakx）_ {\ prism}，\ overline \ calo _ {\ prism} [\ frac {1} {p} {p}] $的全局等价性$ \ hig^{\ nil} _*（x）$ x $上的增强higgs捆绑包的$。一路上，我们从$ \ hig^{\ nil} _*（x）$构造一个倒数$ \ vect（x _ {\ proet}，\ wideHat \ calo_x）$ of $ x $上的广义表示，结果完全是忠实的。
Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic generic fiber $X$. We obtain a global equivalence between the category $\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational Hodge--Tate crystals on the absolute prismatic site $(\frakX)_{\Prism}$ and the category $\HIG^{\nil}_*(X)$ of enhanced Higgs bundles on $X$. Along the way, we construct an inverse Simpson functor from $\HIG^{\nil}_*(X)$ to the category $\Vect(X_{\proet},\widehat\calO_X)$ of generalised representations on $X$, which turns out to be fully faithful.
