The geometric Satake equivalence for integral motives
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915726745403392 |
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| author | Cass, Robert Hove, Thibaud van den Scholbach, Jakob |
| author_facet | Cass, Robert Hove, Thibaud van den Scholbach, Jakob |
| contents | We prove the geometric Satake equivalence for mixed Tate motives over the integral motivic cohomology spectrum. This refines previous versions of the geometric Satake equivalence for split reductive groups. Our new geometric results include Whitney--Tate stratifications of Beilinson--Drinfeld Grassmannians and cellular decompositions of semi-infinite orbits. With future global applications in mind, we also achieve an equivalence relative to a power of the affine line. Finally, we use our equivalence to give Tannakian constructions of Deligne's modification of the dual group and a modified form of Vinberg's monoid over the integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04832 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The geometric Satake equivalence for integral motives Cass, Robert Hove, Thibaud van den Scholbach, Jakob Algebraic Geometry Number Theory Representation Theory We prove the geometric Satake equivalence for mixed Tate motives over the integral motivic cohomology spectrum. This refines previous versions of the geometric Satake equivalence for split reductive groups. Our new geometric results include Whitney--Tate stratifications of Beilinson--Drinfeld Grassmannians and cellular decompositions of semi-infinite orbits. With future global applications in mind, we also achieve an equivalence relative to a power of the affine line. Finally, we use our equivalence to give Tannakian constructions of Deligne's modification of the dual group and a modified form of Vinberg's monoid over the integers. |
| title | The geometric Satake equivalence for integral motives |
| topic | Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2211.04832 |