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THE n-MOTIVIC t-STRUCTURES FOR n = 0, 1 AND 2 JOSEPH AYOUB
 

Summary: THE n-MOTIVIC t-STRUCTURES FOR n = 0, 1 AND 2
JOSEPH AYOUB
Abstract. For a field k and an integer n {0, 1, 2}, we construct a t-structure
n
T M
0(k), n
T M
0(k) on Voevodsky's triangulated category of motives DMeff (k),
which we call the n-motivic t-structure. When n = 0, this is simply the usual
homotopy t-structure, but for n {1, 2}, these are new t-structures. We will show
that the category of Deligne's 1-motives can be embedded as a full subcategory
in the heart of the 1-motivic t-structure. By a rather straightforward analogy, we
are led to specify a class of objects in the heart of the 2-motivic t-structure which
we call mixed 2-motives. We will also check that these objects form an abelian
category.
Keywords: Voevodsky's motives; mixed motives; motivic t-structures.
AMS 2000 Mathematics subject classification: 14F42; 18E10; 19E15.
Contents
Introduction 2
1. Preliminaries 2

  

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

 

Collections: Mathematics