Albanese and Picard 1-motives |
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| Institution: | 1. Dipartimento di Matematica, Università di Geneva, Via Dodecanese, 35, 16146 Genova, Italia;2. Tata Institute of Fundamental Research, School of Mathematics, Homi Bhabba Road, 400 005 Mumbai, India;1. Max-Planck Institute für Mathematik, Bonn, Germany;2. School of Mathematical Sciences, University of Science and Technology of China, 230026 Hefei, China;3. School of Mathematical Scineces, Capital Normal University, 105 Xisanhuanbeilu, 100048 Beijing, China;1. Department of Mathematics, Rikkyo University, Toshimaku, Tokyo, Japan;2. Université de Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, Talence, France |
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| Abstract: | We define, in a purely algebraic way, 1-motives Alb+(X), Alb−(X), Pic+(X), and Pic−(X) associated with any algebraic scheme X over an algebraically closed field of characteristic zero. For X over C of dimension n, the Hodge realizations are, respectively, H2n − 1 (X, Z(n))/(torsion), H1 (X, Z)/(torsion), H1 (X, Z(1)), and H2n − 1 (X, Z(1 n))/(torsion). |
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