论文标题
即使是一般特殊正交组的GALOIS表示
Galois representations for even general special orthogonal groups
论文作者
论文摘要
我们证明存在$ \ mathrm {gspin} _ {2n} $ - 有价值的galois表示形式，与$ \ mathrm {gso} _ {gso} _ {2n} $的同胞cuspidal cuspidal cuspidal自动形式表示，在当地的档案中，有一个临时的参数是sopothe，searme是一个临时的参数。标准表示。这是基于Abelian类型的Shimura品种的共同体，类型为$ d^{\ Mathbb {h}} $，它是由$ \ Mathrm {gso} _ {2n} $的形式产生的。作为一种应用，在类似的假设下，我们计算自身形态多重性，证明（半）旋转$ l $ functions（一半）延续，并改善$ \ mathrm {so} _ {so} _ {2n} $ - 通过删除外部自动摩尔抗体的含义。
We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type $D^{\mathbb{H}}$, arising from forms of $\mathrm{GSO}_{2n}$. As an application, under similar hypotheses, we compute automorphic multiplicities, prove meromorphic continuation of (half) spin $L$-functions, and improve on the construction of $\mathrm{SO}_{2n}$-valued Galois representations by removing the outer automorphism ambiguity.
