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ERIC Number: ED526025
Record Type: Non-Journal
Publication Date: 2009
Pages: 67
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1095-7318-3
ISSN: N/A
On the Strong Direct Summand Conjecture
McCullough, Jason
ProQuest LLC, Ph.D. Dissertation, University of Illinois at Urbana-Champaign
In this thesis, our aim is the study the Vanishing of Maps of Tor Conjecture of Hochster and Huneke. We mainly focus on an equivalent characterization called the Strong Direct Summand Conjecture, due to N. Ranganathan. Our results are separated into three chapters. In Chapter 3, we prove special cases of the Strong Direct Summand Conjecture in mixed characteristic using knowledge about splittings in lower dimensions. In particular, we show that the vanishing of the first Ext module allows us to lift a splitting in lower dimension and prove the Strong Direct Summand Conjecture. In Chapter 4, we study the related Strong Monomial Conjecture. Extending work of Dutta, we give several reformulations of the Strong Monomial Conjecture and prove the Strong Monomial Conjecture for systems of parameters of a certain form. In Chapter 5, we present a generalization of the Vanishing Maps of Tor Conjecture and prove the equicharacteristic case. We then give a shorter proof of the Strong Direct Summand Conjecture. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A