论文标题
P-Adic Hodge理论中弱的基因座和牛顿分层
Weakly admissible locus and Newton stratification in p-adic Hodge theory
论文作者
论文摘要
基本可允许的基因座$ \ MATHCAL {f}（g，μ，b）^a $在国旗品种$ \ MATHCAL {f}（g，μ）$内，与还原的组$ g $一起使用，带有niguscule cocharacter $ g $ $ g $ $ g $，是$ p $ p $ p $ p $ p $ - $ p $ -Adical of-p $ -adic-ad的复杂分析时期。它具有代数近似值$ \ MATHCAL {F}（G，μ，B）^{wa} $在标志品种中，称为弱被允许的基因座。在国旗品种上，$ \ Mathcal {f}（g，μ）$，我们有牛顿分层，该分层以可允许的基因座作为其独特的开放层。在本文中，我们研究了牛顿层与弱化的基因座之间的关系。我们表明，$ \ Mathcal {f}（g，μ，b）^{wa} $是最大的（从某种意义上说，它是牛顿层的一个结合）等于$（g，μ）$弱的全hn-hn-decompososable，它也相当于牛顿分层的条件，即牛顿分层是高度的narerynarasimhan trate tater ander-narsimhan tratsifitive。这些等效条件是完全可解释的条件和弱接近条件的概括。此外，我们给出一个标准，以确定牛顿层是否完全包含在涉及$ g $捆绑的弱化的基因座中，这是$ m $ $ $捆的扩展名，而$ m $捆绑在Fargues-Fontaine曲线上，其中$ m $是$ g $的levi子组。当$ g = \ mathrm {gl} _n $时，我们还提供了一个组合电感标准，以确定fargues-fontaine曲线上的向量捆绑包是否是两个给定向量捆绑包的扩展。
The basic admissible locus $\mathcal{F}(G, μ, b)^a$ inside the flag variety $\mathcal{F}(G, μ)$, attached to a reductive group $G$ with a minuscule cocharacter $μ$ of $G$, is a $p$-adic analogue of the complex analytic period spaces. It has an algebraic approximation $\mathcal{F}(G, μ, b)^{wa}$ inside the flag variety, called the weakly admissible locus. On the flag variety $\mathcal{F}(G, μ)$, we have the Newton stratification which has the admissible locus as its unique open stratum. In this paper, we study the relation between the Newton strata and the weakly admissible locus. We show that $\mathcal{F}(G, μ, b)^{wa}$ is maximal (in the sense that it's a union of Newton strata) is equivalent to $(G, μ)$ weakly fully HN-decomposable, it's also equivalent to the condition that the Newton stratification is finer than the Harder-Narasimhan stratification. These equivalent conditions are generalizations of the fully HN-decomposable condition and the weakly accessible condition. Moreover, we give a criterion to determine whether a Newton stratum is completely contained in the weakly admissible locus involving $G$-bundles as extensions of $M$-bundles over the Fargues-Fontaine curve, where $M$ is a Levi subgroup of $G$. When $G=\mathrm{GL}_n$, we also give a combinatorial inductive criterion to determine whether a vector bundle over the Fargues-Fontaine curve is an extension of two given vector bundles.
