Horrocks' conjecture and operations on Ext and Tor modules
by Burman, Jennifer, Ph.D., UNIVERSITY OF OREGON, 2010, 50 pages; 3420443

Abstract:

Let k be a field, let R = k[x1,...,xn], let [special characters omitted] denote the maximal graded ideal, and let M be a finite-length graded R-module. Horrocks' conjecture says that the ith Betti number of M must be at least ([special characters omitted]). In this dissertation we identify and correct several errors in a paper by Chang which proved Horrocks' conjecture for exponent-two modules, i.e., modules for which [special characters omitted]M = 0. We also define and study operations on Ext*( M, k) and Tor∗ (M, k) and investigate ways they might help prove Horrocks' conjecture in more cases.

 
AdviserDaniel Dugger
SchoolUNIVERSITY OF OREGON
SourceDAI/B 71-09, p. , Sep 2010
Source TypeDissertation
SubjectsMathematics; Theoretical mathematics
Publication Number3420443
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:3420443
  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.