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Forms of homogeneous spherical varieties

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TitleInfo
Title
Forms of homogeneous spherical varieties
Name (type = personal)
NamePart (type = family)
Wang
NamePart (type = given)
Junqi
NamePart (type = date)
1987-
DisplayForm
Junqi Wang
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Mao
NamePart (type = given)
Zhengyu
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Zhengyu Mao
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Advisory Committee
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chair
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Sakellaridis
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Yiannis
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Yiannis Sakellaridis
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Advisory Committee
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internal member
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Sturm
NamePart (type = given)
Jacob
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Jacob Sturm
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Advisory Committee
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internal member
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NamePart (type = family)
van Steirteghem
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Bart
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Bart van Steirteghem
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Advisory Committee
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outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - Newark
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2018
DateOther (qualifier = exact); (type = degree)
2018-01
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2018
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
Let G be a connected reductive algebraic group, spherical G-varieties are generalizations of symmetric G-spaces bearing nice properties on their compactifications. Over an algebraically closed field of characteristic 0, spherical varieties are classified by the Luna-Vust theory (spherical embeddings) together with combinatorial objects called the Luna data (homogeneous spherical varieties). A homogeneous spherical G-variety X can be determined, up to isomorphisms, by its corresponding Luna datum Λ (G,X) . In the first part of this work, Galois cohomology is used to study the spherical varieties over a general field k of characteristic 0, called k-forms of spherical varieties. We start from a homogeneous spherical G-variety X defined over k, with quasi-split G, then it is proven that there is a one-to-one correspondence between the set of k-forms (G ′ ,X ′ ) with a group G ′ which is quasi-split over k, up to k-isomorphisms, and the (continuous) cocycle classes in the first Galois cohomology of the automorphism group of the Luna datum. As an application, in the second part, the Luna data satisfying the transitivity of the automorphism group action on the set of spherical roots are classified. With the transitivity condition, the k-forms corresponding to the sets of the first Galois cohomology of the automorphism group of these Luna data contains all the spherical varieties over k which is of k-rank 1, according to the main theorem in the first part.
Subject (authority = RUETD)
Topic
Mathematical Sciences
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_8606
PhysicalDescription
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (vii, 89 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Junqi Wang
RelatedItem (type = host)
TitleInfo
Title
Graduate School - Newark Electronic Theses and Dissertations
Identifier (type = local)
rucore10002600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T31V5J4B
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Wang
GivenName
Junqi
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2018-01-03 09:31:10
AssociatedEntity
Name
Junqi Wang
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - Newark
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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Technical

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2018-01-03T15:09:10
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2018-01-03T15:09:10
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