论文标题
shtukas堆栈的整体系数
Cohomology with integral coefficients of stacks of shtukas
论文作者
论文摘要
我们通过$ \ mathbb z _ {\ ell} $的系数紧凑地支持SHTUKAS堆栈的共同体组。我们构建了Cuspidal的共同体学组，并证明它们是有限类型的$ \ Mathbb z _ {\ ell} $ - 模块。我们证明，共同体组是具有$ \ Mathbb z _ {\ ell} $系数的Hecke代数上有限类型的模块。 作为一个应用程序，我们证明了具有$ \ Mathbb Q _ {\ ell} $的Cuspidal共同体组 - 系数等于Hecke-Finite共同体学组，具有$ \ Mathbb q _ {\ ell} $ - 系数。 我们还陈述了具有$ \ mathbb z _ {\ ell} $的同事组的Eichler-Shimura关系 - 系数，并证明了偏移操作员的兼容性和恒定的术语形态。
We construct the cohomology groups with compact support of stacks of shtukas with $\mathbb Z_{\ell}$-coefficients. We construct the cuspidal cohomology groups and prove that they are $\mathbb Z_{\ell}$-modules of finite type. We prove that the cohomology groups are modules of finite type over a Hecke algebra with $\mathbb Z_{\ell}$-coefficients. As an application, we prove that the cuspidal cohomology groups with $\mathbb Q_{\ell}$-coefficients are equal to the Hecke-finite cohomology groups with $\mathbb Q_{\ell}$-coefficients defined by V. Lafforgue. We also state the Eichler-Shimura relations for cohomology groups with $\mathbb Z_{\ell}$-coefficients and prove the compatibility of the excursion operators and the constant term morphisms.
