论文标题
Galois表示的Zig-Zag
Zig-zag for Galois Representations
论文作者
论文摘要
Zig-Zag的猜想说，$ {\ mathbb {q}} _ p $的二维晶体表示的减少，大量特殊权重和半整合斜率的降低，最多可通过不合制的$ puce $ pp $ pp $ pp $ p. $ p. $ p. $ puly。我们证明了这种猜想在$ p \ geq 5 $的情况下平稳变化的家庭中。该证明使用Chitrao-Ghate-Yasuda引起的限制性论点，以减少最多$ P+1 $的半稳定体重表示，然后吸引Breuil-Mézard，Guerberoff-Park和Chitrao-Ghate的工作。
The zig-zag conjecture says that the reductions of two-dimensional crystalline representations of the Galois group of ${\mathbb {Q}}_p$ of large exceptional weights and half-integral slopes up to $\frac{p-1}{2}$ vary through an alternating sequence of irreducible and reducible mod $p$ representations. We prove this conjecture in smoothly varying families of such representations for $p \geq 5$. The proof uses a limiting argument due to Chitrao-Ghate-Yasuda to reduce to the case of semi-stable representations of weights at most $p+1$, and then appeals to the work of Breuil-Mézard, Guerberoff-Park and Chitrao-Ghate.
