论文标题
Fontaine-Laffaille范围内的G值晶体变形环
G-Valued Crystalline Deformation Rings in the Fontaine-Laffaille Range
论文作者
论文摘要
让$ g $为一个$ p $ - adiC字段中的整数上的拆分还原组，带有残基字段$ \ mathbf {f} $。修复$ \ mathbf {q} _p $的未经密码扩展名的绝对Galois组的表示$ \Overlineρ$，价值为$ g（\ Mathbf {f}）$。我们研究了$ \Overlineρ$的结晶变形环，其中固定的$ p $ -ADIC HODGE类型满足Fontaine-Laffaille条件的类似物，以$ G $可估算的表示形式。特别是，我们在$ p $ -ADIC HODGE类型上给出了根理论条件，以确保晶体变形环正式光滑。我们的结果改善了经典组而不是A型的所有已知结果，并为特殊组提供了第一个此类结果。
Let $G$ be a split reductive group over the ring of integers in a $p$-adic field with residue field $\mathbf{F}$. Fix a representation $\overlineρ$ of the absolute Galois group of an unramified extension of $\mathbf{Q}_p$, valued in $G(\mathbf{F})$. We study the crystalline deformation ring for $\overlineρ$ with a fixed $p$-adic Hodge type that satisfies an analog of the Fontaine-Laffaille condition for $G$-valued representations. In particular, we give a root theoretic condition on the $p$-adic Hodge type which ensures that the crystalline deformation ring is formally smooth. Our result improves on all known results for classical groups not of type A and provides the first such results for exceptional groups.
