Albanese and Picard 1-motives

Luca Barbieri Viale; Vasudevan Srinivas

doi:10.1016/s0764-4442(98)80399-6

Albanese and Picard 1-motives

Luca Barbieri Viale
, Vasudevan Srinivas

Mathematics

University of Genoa

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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, H^2n-1(X, Z(n))/(torsion), H₁(X, Z)/(torsion), H¹(X, Z(1)), and H_2n-1(X, Z(1 - n))/(torsion).

Original language	English
Pages (from-to)	1397-1401
Number of pages	5
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	326
Issue number	12
DOIs	https://doi.org/10.1016/s0764-4442(98)80399-6
State	Published - Jun 1998

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title = "Albanese and Picard 1-motives",

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).",

author = "\{Barbieri Viale\}, Luca and Vasudevan Srinivas",

year = "1998",

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doi = "10.1016/s0764-4442(98)80399-6",

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AU - Barbieri Viale, Luca

AU - Srinivas, Vasudevan

PY - 1998/6

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N2 - 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).

AB - 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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U2 - 10.1016/s0764-4442(98)80399-6

DO - 10.1016/s0764-4442(98)80399-6

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SN - 0764-4442

VL - 326

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JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 12

ER -

Albanese and Picard 1-motives

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