Local-global compatibility and the action of monodromy on nearby cycles
Local-global compatibility and the action of monodromy on nearby cycles
复制标题
局部-全局兼容性以及单调性对附近周期的作用
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Caraiani
中科院分区：
文献类型：
--
作者：
A. Caraiani
在n为偶数且l为6维p的情况下，我们加强了GLn的Langlands对应的局部-全局相容性。是GLn.AL/的尖点自守表示，它是共轭自对偶的。假设... 1是上同调的，而不是Shin定义的“稍微正则”。在这种情况下，Chenevier和Harris构造了一个l-adic Galois表示Rl..并证明了在素数v不整除l时的局部-整体相容性。我们通过证明Rl的限制的Frobenius半简化来扩展这种兼容性。在v处的分解群对应于...的图像。v通过当地的朗兰兹通信。我们遵循泰勒和吉田的策略，假设...在有限的地方平方可积。为了使论证工作，我们研究的行动的monodromy运营商N上的复杂的附近的周期计划，这是局部稳定的产品严格半稳定计划，我们得到了推广的重量谱序列在这种情况下。我们还证明了Ramanujan-Petersson猜想.同上。
We strengthen the local-global compatibility of Langlands correspondences for GLn in the case when n is even and l 6D p. Let L be a CM field, and let ... be a cuspidal automorphic representation of GLn.AL/ which is conjugate self-dual. Assume that...1 is cohomological and not “slightly regular,” as defined by Shin. In this case, Chenevier and Harris constructed an l-adic Galois representationRl..../ and proved the local-global compatibility up to semisimplification at primes v not dividing l . We extend this compatibility by showing that the Frobenius semisimplification of the restriction of Rl..../ to the decomposition group at v corresponds to the image of ...v via the local Langlands correspondence. We follow the strategy of Taylor and Yoshida, where it was assumed that ... is square-integrable at a finite place. To make the argument work, we study the action of the monodromy operator N on the complex of nearby cycles on a scheme which is locally etale over a product of strictly semistable schemes and we derive a generalization of the weight spectral sequence in this case. We also prove the Ramanujan–Petersson conjecture for ... as above.