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Slice filtration and torsion theory in motivic cohomology

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TitleInfo
Title
Slice filtration and torsion theory in motivic cohomology
Name (type = personal)
NamePart (type = family)
Fu
NamePart (type = given)
Knight
NamePart (type = date)
1984-
DisplayForm
Knight Fu
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Weibel
NamePart (type = given)
Charles
DisplayForm
Charles Weibel
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Buch
NamePart (type = given)
Anders
DisplayForm
Anders Buch
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Borisov
NamePart (type = given)
Lev
DisplayForm
Lev Borisov
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Grayson
NamePart (type = given)
Daniel
DisplayForm
Daniel Grayson
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We show that the category HI of homotopy invariant Nisnevich sheaves with transfers and the category CycMod are each equipped with a strong filtrations and a strong cofiltration. To do so, we first define pre-coradicals and coradicals on well-powered abelian categories, and show that every isomorphism class of coradical is associated to a canonical torsion theory. We then summarize the theory of motivic cohomology needed to define HI, its symmetric monoidal structure and its partial internal hom. Along the way, we recall the construction of the slice filtration on DM^{eff,−}, and extend the filtration structure on DM^{eff,−} to DM. We then define and construct the torsion filtration on HI by constructing a sequence of coradicals. We explain how the torsion filtration is related to the slice filtration on DM^{eff,−}. We extend the torsion filtration to the category HI_* of homotopic modules. Appealing to the categorical equivalence between HI_* and CycMod, we obtain the torsion filtration on CycMod. Finally, we generalize the conditions under which torsion filtrations exist for the heart of a tensor triangulated category.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5516
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
vi, 106 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Knight Fu
Subject (authority = ETD-LCSH)
Topic
Torsion theory (Algebra)
Subject (authority = ETD-LCSH)
Topic
Cohomology operations
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3ST7N58
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Fu
GivenName
Knight
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-15 10:07:57
AssociatedEntity
Name
Knight Fu
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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