# 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

Mathematics

Classification

0364: Applied Mathematics

0405: 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