论文标题
霍奇 - 泰特棱镜晶体和森理论
Hodge-Tate prismatic crystals and Sen theory
论文作者
论文摘要
让$ k $是具有完美残留场的混合特征完整的离散估值字段，让$ k_ \ infty/k $成为Kummer Tower的扩展，通过毗邻$ p $ p $ p $ p $ popper rots的均匀均匀均匀均匀的均匀器。我们使用这个kummer塔来重建森理论，该理论是使用循环塔获得的。我们在库默塔上使用了这种森理论，我们证明了Min-Wang的猜想，该猜想预测hodge-tate Prismatic晶体是由Sen Operators确定的。这意味着（理性）霍奇特（Hodge-tate）棱柱形晶体的类别等同于几乎霍奇特（Hodge-tate）表示的类别。
Let $K$ be a mixed characteristic complete discrete valuation field with perfect residue field, and let $K_\infty/K$ be a Kummer tower extension by adjoining a compatible system of $p$-power roots of a chosen uniformizer. We use this Kummer tower to reconstruct Sen theory which classically is obtained using the cyclotomic tower. Using this Sen theory over the Kummer tower, we prove a conjecture of Min-Wang which predicts that Hodge-Tate prismatic crystals are determined by the Sen operator; this implies that the category of (rational) Hodge-Tate prismatic crystals is equivalent to the category of nearly Hodge-Tate representations.
