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arXiv 2001.05805math.AGmath.RT
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shtukas 层的整系数上同调

Cohomology with integral coefficients of stacks of shtukas

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备注：
Added the Eichler-Shimura relations for cohomology groups with $\mathbb Z_{\ell}$-coefficients
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AI总结：

本文构造了 shtukas 层的整系数紧支上同调与尖点上同调，证明其为有限型模，并应用于证明与 Lafforgue 定义的 Hecke 有限上同调相等，同时给出 Eichler-Shimura 关系及算子相容性。

摘要：

我们构造了具有 $\mathbb Z_{\ell}$ 系数的 shtukas 层的紧支上同调群。我们构造了尖点上同调群，并证明了它们是有限型的 $\mathbb Z_{\ell}$ 模。我们证明了这些上同调群是带有 $\mathbb Z_{\ell}$ 系数的 Hecke 代数上的有限型模。作为应用，我们证明了具有 $\mathbb Q_{\ell}$ 系数的尖点上同调群等于由 V. Lafforgue 定义的具有 $\mathbb Q_{\ell}$ 系数的 Hecke 有限上同调群。我们还陈述了具有 $\mathbb Z_{\ell}$ 系数的上同调群的 Eichler-Shimura 关系，并证明了 excursion 算子与常数项态射的相容性。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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