# 1-motivic sheaves and the Albanese functor

Ayoub, J; Barbieri-Viale, L (2009). 1-motivic sheaves and the Albanese functor. Journal of Pure and Applied Algebra, 213(5):809-839.

## Abstract

Using sheaf theoretic methods, we define functors View the MathML source and View the MathML source. The functor View the MathML source extends the one in [L. Barbieri-Viale, B. Kahn, On the derived category of 1-motives, I. Prépublication Mathématique de l’IHÉS (M/07/22), June 2007, 144 pages] to non-necessarily geometric motives. These functors are then used to define higher Néron–Severi groups and higher Albanese sheaves.

## Abstract

Using sheaf theoretic methods, we define functors View the MathML source and View the MathML source. The functor View the MathML source extends the one in [L. Barbieri-Viale, B. Kahn, On the derived category of 1-motives, I. Prépublication Mathématique de l’IHÉS (M/07/22), June 2007, 144 pages] to non-necessarily geometric motives. These functors are then used to define higher Néron–Severi groups and higher Albanese sheaves.

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