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1-MOTIVIC SHEAVES AND THE ALBANESE JOSEPH AYOUB AND LUCA BARBIERI-VIALE
 

Summary: 1-MOTIVIC SHEAVES AND THE ALBANESE
FUNCTOR
JOSEPH AYOUB AND LUCA BARBIERI-VIALE
Abstract. Using sheaf theoretic methods, we define functors
L0 : DMeff(k) D(HI0(k)) and LAlb : DMeff(k)
D(HI1(k)). The functor LAlb extends the one in [3] to non-
necessarily geometric motives. These functors are then used to
define higher N´eron-Severi groups and higher Albanese sheaves.
Contents
Introduction 1
1. n-generated sheaves 5
2. Deriving 0 and Alb 29
3. Computations and applications 47
References 53
Introduction
For a field k, say perfect, and a Grothendieck topology on the cate-
gory of smooth k-schemes, such as the Nisnevich or the ´etale topology,
we denote by Shv
tr(k) the abelian category of -sheaves with transfers
on Sm/k. Following Voevodsky, we consider DM

  

Source: Ayoub, Joseph - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics