IWR and Mathematical Institute, Ruprecht-Karls-Universität Heidelberg, Heidelberg 69120, Germany.
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218.
Proc Natl Acad Sci U S A. 2023 Mar 28;120(13):e2221042120. doi: 10.1073/pnas.2221042120. Epub 2023 Mar 20.
We show that crystalline points are Zariski dense in the deformation space of a representation of the absolute Galois group of a -adic field. We also show that these points are dense in the subspace parameterizing deformations with the determinant equal to a fixed crystalline character. Our proof is purely local and works for all -adic fields and all residual Galois representations.
我们证明了在一个 -adic 域的绝对伽罗瓦群的表示的形变空间中，晶态点是 Zariski 稠密的。我们还证明了这些点在参数化行列式等于固定晶态特征的形变子空间中是稠密的。我们的证明是纯粹局部的，适用于所有 -adic 域和所有剩余伽罗瓦表示。
