论文标题
De Rham Prismatic Crystals $ \ Mathcal {O} _K $
De Rham prismatic crystals over $\mathcal{O}_K$
论文作者
论文摘要
我们在$（\ Mathcal {o} _K）_ {\bboldΔ} $上研究De Rham Prismatic晶体。我们表明，de rham晶体由一系列矩阵$ \ {a_ {m，1} \} _ {m \ geq 0} $带有$ a_ {0,1} $“ nilpotent”。使用此情况，我们证明了从$（\ Mathcal {o} _K）_ {\bboldΔ} $上的自然函数到几乎de rham表示的类别是完全忠实的。关键成分是$ g_k $的de rham表示的sen样式变形定理。
We study de Rham prismatic crystals on $(\mathcal{O}_K)_{\bboldΔ}$. We show that a de Rham crystal is controlled by a sequence of matrices $\{A_{m,1}\}_{m \geq 0}$ with $A_{0,1}$ "nilpotent". Using this, we prove that the natural functor from de Rham crystals over $(\mathcal{O}_K)_{\bboldΔ}$ to the category of nearly de Rham representations is fully faithful. The key ingredient is a Sen style decompletion theorem for de Rham representations of $G_K$.
