Zero Cycles of Degree One on Principal Homogeneous Spaces
by Black, Jodi A., Ph.D., EMORY UNIVERSITY, 2011, 87 pages; 3465025

Abstract:

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.
 
AdviserParimala Raman
SchoolEMORY UNIVERSITY
SourceDAI/B 72-10, p. , Aug 2011
Source TypeDissertation
SubjectsApplied mathematics; Mathematics
Publication Number3465025
Adobe PDF Access the complete dissertation:
 

» Find an electronic copy at your library.
  Use the link below to access a full citation record of this graduate work:
  http://gateway.proquest.com/openurl%3furl_ver=Z39.88-2004%26res_dat=xri:pqdiss%26rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation%26rft_dat=xri:pqdiss:3465025
  If your library subscribes to the ProQuest Dissertations & Theses (PQDT) database, you may be entitled to a free electronic version of this graduate work. If not, you will have the option to purchase one, and access a 24 page preview for free (if available).

About ProQuest Dissertations & Theses
With over 2.3 million records, the ProQuest Dissertations & Theses (PQDT) database is the most comprehensive collection of dissertations and theses in the world. It is the database of record for graduate research.

The database includes citations of graduate works ranging from the first U.S. dissertation, accepted in 1861, to those accepted as recently as last semester. Of the 2.3 million graduate works included in the database, ProQuest offers more than 1.9 million in full text formats. Of those, over 860,000 are available in PDF format. More than 60,000 dissertations and theses are added to the database each year.

If you have questions, please feel free to visit the ProQuest Web site - http://www.proquest.com - or call ProQuest Hotline Customer Support at 1-800-521-3042.