English

Albanese and Picard 1-motives

Algebraic Geometry 2007-05-23 v1

Abstract

We define, in a purely algebraic way, 1-motives Alb+(X)Alb^{+}(X), Alb(X)Alb^{-}(X), Pic+(X)Pic^{+}(X) and Pic(X)Pic^{-}(X) associated with any algebraic scheme XX over an algebraically closed field of characteristic zero. For XX over \C\C of dimension nn the Hodge realizations are, respectively, H2n1(X)(n)H^{2n-1}(X)(n), H1(X)H_{1}(X), H1(X)(1)H^{1}(X)(1) and H2n1(X)(1n)H_{2n-1}(X)(1-n).

Keywords

Cite

@article{arxiv.math/9803112,
  title  = {Albanese and Picard 1-motives},
  author = {L. Barbieri Viale and V. Srinivas},
  journal= {arXiv preprint arXiv:math/9803112},
  year   = {2007}
}

Comments

5 pages, LaTeX, submitted as CR Note