Big pictures of motivic and classical homotopy theories
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910285541933056 |
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| author | Rouintan, Ahmad |
| author_facet | Rouintan, Ahmad |
| contents | Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's triangulated category of motives. A connection that is the motivic analogue of the connection between algebraic topology and homological algebra. In this paper, we try to understand the big picture of motivic homotopy theory and its connection to Voevodsky's motives by comparison to the classical counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18993 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Big pictures of motivic and classical homotopy theories Rouintan, Ahmad Algebraic Geometry Algebraic Topology Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's triangulated category of motives. A connection that is the motivic analogue of the connection between algebraic topology and homological algebra. In this paper, we try to understand the big picture of motivic homotopy theory and its connection to Voevodsky's motives by comparison to the classical counterpart. |
| title | Big pictures of motivic and classical homotopy theories |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2310.18993 |