Local duality theorems for commutative algebraic groups
| Autor: | Gonzalez-Aviles, Cristian D. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Minor changes to the presentation. Still 37 pages |
| Databáze: | arXiv |
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