谱Hecke代数
The Spectral Hecke Algebra
摘要：
我们介绍了一个派生的增强局部伽罗瓦变形环，我们称之为“光谱Hecke代数”，在类比的几何朗兰兹计划的建设。这是一个作用于朗兰兹对应的谱侧的赫克代数，即作用于伽罗瓦表示的模空间。证明了谱Hecke代数在Galatius-Venkatesh的导出Galois变形环上的作用与Venkatesh的导出Hecke代数在算术群的上同调上的作用之间的导出局部-整体相容性的最简单形式.
英文摘要：
We introduce a derived enhancement of local Galois deformation rings that we call the "spectral Hecke algebra", in analogy to a construction in the Geometric Langlands program. This is a Hecke algebra that acts on the spectral side of the Langlands correspondence, i.e. on moduli spaces of Galois representations. We verify the simplest form of derived local-global compatibility between the action of the spectral Hecke algebra on the derived Galois deformation ring of Galatius-Venkatesh, and the action of Venkatesh's derived Hecke algebra on the cohomology of arithmetic groups.
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