Abstract
AbstractWe characterize the tempered part of the automorphic Langlands category $$\mathfrak {D}({\text {Bun}}_G)$$
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 $$\Sigma $$
Σ
a smooth affine curve, the Borel–Moore homology of the indscheme $${\text {Maps}}(\Sigma ,G)$$
Maps
(
Σ
,
G
)
vanishes.
Publisher
Springer Science and Business Media LLC
Reference42 articles.
1. Arinkin, D., Gaitsgory, D.: Singular support of coherent sheaves and the geometric Langlands conjecture. Selecta Math. (N.S.) 21(1), 1–199 (2015)
2. Arinkin, D., Gaitsgory, D.: The category of singularities as a crystal and global Springer fibers. J. Am. Math. Soc. 31(1), 135–214 (2018)
3. Beauville, A., Laszlo, Y.: Un lemme de descente. Comptes Rendus Acad. Sci. Paris 320, 335–340 (1995)
4. Barlev, J.: D-modules on spaces of rational maps. Compos. Math. 150, 835–876 (2014)
5. Beilinson, A., Drinfeld, V.: Chiral Algebras, vol. 51. American Mathematical Society Colloquium Publications (2004)
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