Tensor structure on smooth motives

Permanent URL: http://hdl.handle.net/2047/d20000154
Title:
Tensor structure on smooth motives
Creator:
Banerjee, Anandam (Author)
Contributor:
Levine, Marc, 1952- (Advisor)
Publisher:
Boston, Massachusetts : Northeastern University, 2010
Date Accepted:
April 2010
Date Awarded:
May 2010
Type of resource:
Text
Genre:
Dissertations
Format:
electronic
Digital origin:
born digital
Abstract/Description:
Grothendieck first defined the notion of a "motif" as a way of finding a universal cohomology theory for algebraic varieties. Although this program has not been realized, Voevodsky has constructed a triangulated category of geometric motives over a perfect field, which has many of the properties expected of the derived category of the conjectural abelian category of motives. The construction of the triangulated category of motives has been extended by Cisinski-Deglise to a triangulated category of motives over a base-scheme S. Recently, Bondarko constructed a DG category of motives, whose homotopy category is equivalent to Voevodsky's category of effective geometric motives, assuming resolution of singularities. Soon after, Levine extended this idea to construct a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S-schemes, assuming that S is itself smooth over a perfect field. In both constructions, the tensor structure requires coefficients. In my thesis, I show how to provide a tensor structure on the homotopy category mentioned above, when S is semilocal and essentially smooth over a field of characteristic zero. This is done by defining a pseudo-tensor structure on the DG category of motives constructed by Levine, which induces a tensor structure on its homotopy category.
Subjects and keywords:
DG categories
tensor structure
Motives (Mathematics)
Mathematics
DOI:
https://doi.org/10.17760/d20000154
Permanent Link:
http://hdl.handle.net/2047/d20000154
Use and reproduction:
In Copyright: This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the right-holder(s). (http://rightsstatements.org/vocab/InC/1.0/)
Copyright restrictions may apply.

Downloads