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arXiv · 1904.10903

Tempered D-modules and Borel-Moore homology vanishing

Dario Beraldo
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Abstract

We characterize the tempered part of the automorphic Langlands category D-mod(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 supports. 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 $Σ$ a smooth affine curve, the Borel-Moore homology of the indscheme $Maps(Σ,G)$ vanishes.

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Dario Beraldo. 2021-01-15. Tempered D-modules and Borel-Moore homology vanishing. https://doi.org/10.1007/s00222-021-01036-2

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