Abstract/Details

Zero Cycles of Degree One on Principal Homogeneous Spaces


2011 2011

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Abstract (summary)

Let k be a field and let G be a connected linear algebraic group over k. Let X be a principal homogeneous space under G over k. Jean-Pierre Serre has asked the following: "If X admits a zero cycle of degree one, does X have a k-rational point?" We give a positive answer to the question in two settings: 1. The field k is of characteristic different from 2 and the group G is simply connected or adjoint and of classical type. 2. The field k is perfect and of virtual cohomological dimension at most 2 and the simply connected group associated to G satisfies a Hasse principle over k.

Indexing (details)


Subject
Applied Mathematics;
Mathematics
Classification
0364: Applied Mathematics
0405: Mathematics
Identifier / keyword
Applied sciences; Pure sciences; Galois cohomology; Homogeneous spaces; Linear algebraic groups; Zero cycles
Title
Zero Cycles of Degree One on Principal Homogeneous Spaces
Author
Black, Jodi A.
Number of pages
87
Publication year
2011
Degree date
2011
School code
0665
Source
DAI-B 72/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9781124766850
Advisor
Raman, Parimala
Committee member
Garibaldi, Skip; Ono, Ken
University/institution
Emory University
Department
Math and Computer Science
University location
United States -- Georgia
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3465025
ProQuest document ID
881293374
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/881293374
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