论文标题
建造Galois表示形式在一个质量上被淘汰
Constructing Galois representations ramified at one prime
论文作者
论文摘要
令$ n> 1 $，$ e \ geq 0 $和prime Number $ p \ geq 2^{n+2+2e}+3 $，因此规律性$ p $的索引是$ \ leq e $。我们表明，存在无限的许多不可约的galois表示$ρ：gal（\ bar {\ mathbb {q}}}/\ mathbb {q}）\ rightarrow {gl} _n（\ mathbb {q} _p）此外，这些表示形式显示为包含$ {sl} _n（\ Mathbb {z} _p）$的固定有限索引子组。这样的表示是通过在$ {gl} _n中以对角圆环中的图像提起合适的残差表示$ \barρ$来构建的（\ mathbb {f} _p）$，为此，全局变形问题毫无结构。
Let $n>1$, $e\geq 0$ and a prime number $p\geq 2^{n+2+2e}+3$, such that the index of regularity of $p$ is $\leq e$. We show that there are infinitely many irreducible Galois representations $ρ: Gal(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow {GL}_n(\mathbb{Q}_p)$ unramified at all primes $l\neq p$. Furthermore, these representations are shown to have image containing a fixed finite index subgroup of ${SL}_n(\mathbb{Z}_p)$. Such representations are constructed by lifting suitable residual representations $\barρ$ with image in the diagonal torus in ${GL}_n(\mathbb{F}_p)$, for which the global deformation problem is unobstructed.
