论文标题
几何不可还原$ p $ - adiC的本地系统是de rham的扭曲
Geometrically irreducible $p$-adic local systems are de Rham up to a twist
论文作者
论文摘要
我们证明，任何几何不可约的$ \ operline {\ mathbb {q}} _ p $ - 局部系统在$ p $ a的$ k $ k $ a $ k $ of $ p $ k $的角色之后，在$ p $ adic field $ k $ a $ p $ k $ k $ a $ p $ k $上变成。特别是，对于任何几何不可约的$ \ operline {\ mathbb {q}} _ p $ - 局部系统，在一个数字字段上平滑的品种上，基本组的相关投影表示可以自动满足相对fontaine-mazur猜想的假设。证明使用$ P $ -ADIC SIMPSON和DIAO-LAN-LIU-ZHU的Riemann-Hilbert以及Shimizu开发的sen运算师的sen操作员。在此过程中，我们观察到，如果$ k $的平滑几何连接的代数品种在$ k $上的平滑几何连接，则如果其在一个闭合点处的茎是霍迪格·泰特（Hodge-Tate）的代表，则是hodge-tate。此外，我们证明了具有任意几何单曲的局部系统的主要定理版本，这使我们得出结论，基本组的促成代数完成的GALOIS行动是De Rham。
We prove that any geometrically irreducible $\overline{\mathbb{Q}}_p$-local system on a smooth algebraic variety over a $p$-adic field $K$ becomes de Rham after a twist by a character of the Galois group of $K$. In particular, for any geometrically irreducible $\overline{\mathbb{Q}}_p$-local system on a smooth variety over a number field the associated projective representation of the fundamental group automatically satisfies the assumptions of the relative Fontaine-Mazur conjecture. The proof uses $p$-adic Simpson and Riemann-Hilbert correspondences of Diao-Lan-Liu-Zhu and the Sen operator on the decompletions of those developed by Shimizu. Along the way, we observe that a $p$-adic local system on a smooth geometrically connected algebraic variety over $K$ is Hodge-Tate if its stalk at one closed point is a Hodge-Tate Galois representation. Moreover, we prove a version of the main theorem for local systems with arbitrary geometric monodromy, which allows us to conclude that the Galois action on the pro-algebraic completion of the fundamental group is de Rham.
