Tempered D-modules and Borel-Moore homology vanishing

• 成果类型: Article
• 署名作者: Beraldo, Dario
• 署名单位: University of London; University College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01036-2
• 发表日期: 2021
• 页码: 453-528
• 关键词: g-bundles; REPRESENTATIONS; COHOMOLOGY; category; Duality; SPACES; stack

摘要

We characterize the tempered part of the automorphic Langlands category D(Bun(G)) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and Sigma a smooth affine curve, the Borel-Moore homology of the indscheme Maps(Sigma, G) vanishes.