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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.08699 |
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| _version_ | 1866929231317958656 |
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| author | Gonzalez-Aviles, Cristian D. |
| author_facet | Gonzalez-Aviles, Cristian D. |
| contents | If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems that relate the fppf cohomology groups of G to the hypercohomology groups of the k-1-motive $G^{\vee}$. We also obtain a duality theorem for the second cohomology group of an arbitrary k-1-motive. These results have applications (to be discussed elsewhere) to certain extensions of Lichtenbaum-van Hamel duality to a class of non-smooth proper k-varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local duality theorems for commutative algebraic groups Gonzalez-Aviles, Cristian D. Number Theory Algebraic Geometry 11G25, 14G20 If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems that relate the fppf cohomology groups of G to the hypercohomology groups of the k-1-motive $G^{\vee}$. We also obtain a duality theorem for the second cohomology group of an arbitrary k-1-motive. These results have applications (to be discussed elsewhere) to certain extensions of Lichtenbaum-van Hamel duality to a class of non-smooth proper k-varieties. |
| title | Local duality theorems for commutative algebraic groups |
| topic | Number Theory Algebraic Geometry 11G25, 14G20 |
| url | https://arxiv.org/abs/2305.08699 |