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The n-motivic t-structures for n=0,1 and 2


Ayoub, J (2011). The n-motivic t-structures for n=0,1 and 2. Advances in Mathematics, 226(1):111-138.

Abstract

For a field k and an integer n∈{0,1,2}, we construct a t-structure View the MathML source 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.

Abstract

For a field k and an integer n∈{0,1,2}, we construct a t-structure View the MathML source 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 January 2011
Deposited On:14 Nov 2011 14:26
Last Modified:07 Dec 2017 09:38
Publisher:Elsevier
ISSN:0001-8708
Funders:Swiss National Science Foundation (NSF), Grant No. 2000201-124737/1
Publisher DOI:https://doi.org/10.1016/j.aim.2010.06.011

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