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