Six-Functor Formalisms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911391194021888 |
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| author | Scholze, Peter |
| author_facet | Scholze, Peter |
| contents | These are lecture notes for a course in Winter 2022/23, updated and completed in October 2025.
The goal of the lectures is to present some recent developments around six-functor formalisms, in particular: the abstract theory of 6-functor formalisms; the 2-category of cohomological correspondences, and resulting simplifications in the proofs of Poincaré--Verdier duality results; the relation between 6-functor formalisms and ``geometric rings''; many examples of 6-functor formalisms, both old and new. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Six-Functor Formalisms Scholze, Peter Algebraic Geometry Algebraic Topology Category Theory Number Theory 55N30, 18F10, 18F20, 14F42, 14F40, 14F30, 14F20, 14F08, 14A30 These are lecture notes for a course in Winter 2022/23, updated and completed in October 2025. The goal of the lectures is to present some recent developments around six-functor formalisms, in particular: the abstract theory of 6-functor formalisms; the 2-category of cohomological correspondences, and resulting simplifications in the proofs of Poincaré--Verdier duality results; the relation between 6-functor formalisms and ``geometric rings''; many examples of 6-functor formalisms, both old and new. |
| title | Six-Functor Formalisms |
| topic | Algebraic Geometry Algebraic Topology Category Theory Number Theory 55N30, 18F10, 18F20, 14F42, 14F40, 14F30, 14F20, 14F08, 14A30 |
| url | https://arxiv.org/abs/2510.26269 |