Let K be the field of fractions of a complete discrete valuation ring \( \mathcal{A} \) with residue field k, and let G be a connected reductive algebraic group over K. Suppose \( \mathcal{P} \) is a parahoric group scheme attached to G. In particular, \( \mathcal{P} \) is a smooth affine \( \mathcal{A} \)-group scheme having generic fiber \( \mathcal{P} \)_K = G; the group scheme \( \mathcal{P} \) is in general not reductive over \( \mathcal{A} \).If G splits over an unramified extension of K, we find in this paper a closed and reductive \( \mathcal{A} \)-subgroup scheme \( \mathcal{M}\subset \mathcal{P} \) for which the special fiber \( \mathcal{M} \)_k is a Levi factor of \( \mathcal{P} \)_k. Moreover, we show that the generic fiber \( M={\mathcal{M}}_{\mathrm{K}} \) is a subgroup of G which is geometrically of type C(μ) – i.e., after a separable field extension, M is the identity component \( M={C}_G^o\left(\phi \right) \) of the centralizer of the image of a homomorphism ϕ: μ_n → H, where μ_n is the group scheme of n-th roots of unity for some n ≥ 2. For a connected and split reductive group H over any field \( \mathcal{F} \), the paper describes those subgroups of H which are of type C(μ).

中文翻译：

---

似群群方案的还原子群方案

令K为残差场为k的完整离散估值环\（\ mathcal {A} \）的分数场，令G为K之上的连通还原代数群。假设\（\ mathcal {P} \）为G附带的准马群计划。特别地，\（\ mathcal {P} \）是具有仿射光纤\（\ mathcal {P} \）_K = G的光滑仿射\（\ mathcal {A} \）-群方案。分组方案\（\ mathcal {P} \）通常不归约于\（\ mathcal {A} \）。如果G分裂成K的无分支扩展，我们在本文中发现一个封闭且归约的\（\ mathcal {A} \）-子组方案\（\ mathcal {M} \ subset \ mathcal {P} \），其中特殊纤维\（\ mathcal {M} \）_k是李维因子\（ \ mathcal {P} \）_k。此外，我们证明通用光纤\（M = {\ mathcal {M}} _ {\ mathrm {K}} \）是G的一个子群，其几何类型为C（μ）–即，在可分离场之后延伸，中号是身份组件\（M = {C} _G = O \左（\披\右）\）同态的图像的扶正φ：μ _ñ → ħ，其中μ_Ñ是组成的组方案Ñ -统一的第根一些Ñ≥ 2.对于连接和分离还原基ħ任意域\（\ mathcal {F} \） ，本文描述的那些亚组ħ其是类型的C（μ）。