Abelian motives and Shimura varieties in nonzero characteristic
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915550575198208 |
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| author | Milne, James S. |
| author_facet | Milne, James S. |
| contents | Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abelian motives and Shimura varieties in nonzero characteristic Milne, James S. Algebraic Geometry Number Theory 14C15 Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences. |
| title | Abelian motives and Shimura varieties in nonzero characteristic |
| topic | Algebraic Geometry Number Theory 14C15 |
| url | https://arxiv.org/abs/2508.09972 |