Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.08504 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915295828901888 |
|---|---|
| author | Nocera, Guglielmo |
| author_facet | Nocera, Guglielmo |
| contents | Let $G$ be a complex reductive group. The spherical Hecke category of $G$ can be presented as the category of $G_{\mathcal O}$-equivariant constructible sheaves on the affine Grassmannian $\mathrm{Gr}_G$. This category admits a convolution product, extending the convolution product of equivariant perverse sheaves. In this paper, we upgrade the mentioned convolution product to a left t-exact $\mathbb E_3$-monoidal structure in $\infty$-categories. The construction is intrinsic to the automorphic side. Our main tools are the Beilinson--Drinfeld Grassmannian, Lurie's characterization of $\mathbb E_k$-algebras via the topological Ran space, the homotopy theory of stratified spaces, and the formalism of correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_08504 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A model for the E3 fusion-convolution product of constructible sheaves on the affine Grassmannian Nocera, Guglielmo Algebraic Geometry 14D24, 57N80, 18N70, 22E57, 32S60 Let $G$ be a complex reductive group. The spherical Hecke category of $G$ can be presented as the category of $G_{\mathcal O}$-equivariant constructible sheaves on the affine Grassmannian $\mathrm{Gr}_G$. This category admits a convolution product, extending the convolution product of equivariant perverse sheaves. In this paper, we upgrade the mentioned convolution product to a left t-exact $\mathbb E_3$-monoidal structure in $\infty$-categories. The construction is intrinsic to the automorphic side. Our main tools are the Beilinson--Drinfeld Grassmannian, Lurie's characterization of $\mathbb E_k$-algebras via the topological Ran space, the homotopy theory of stratified spaces, and the formalism of correspondences. |
| title | A model for the E3 fusion-convolution product of constructible sheaves on the affine Grassmannian |
| topic | Algebraic Geometry 14D24, 57N80, 18N70, 22E57, 32S60 |
| url | https://arxiv.org/abs/2012.08504 |