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Duality of Albanese and Picard 1-motives | | Niranjan Ramachandran
; | | Date: |
8 Apr 1998 | | Subject: | Algebraic Geometry; K-Theory and Homology; Number Theory MSC-class: 14K30;14K15;11G45 | math.AG math.KT math.NT | | Affiliation: | U. of Maryland, College Park | | Abstract: | We define Albanese and Picard 1-motives of smooth (simplicial) schemes over a perfect field. For smooth proper schemes, these are the classical Albanese and Picard varieties. For a curve, these are t he homological 1-motive of Lichtenbaum and the motivic $H^1$ of Deligne. This paper proves a conjecture of Deligne about providing an algebraic description, via 1-motives, of the first homology and cohomology groups of a complex algebraic variety. (L. Barbieri-Viale and V. Srinivas have also proved this independently.) It also contains a purely algebraic proof of Lichtenbaum’s conjecture that the Albanese and the Picard 1-motives of a (simplicial) scheme are dual. This gives a new proof of an unpublished theorem of Lichtenbaum that Deligne’s 1-motive of a curve is dual to Lichtenbaum’s 1-motive. | | Source: | arXiv, math.AG/9804042 | | Services: | Forum | Review | PDF | Favorites | |
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