Topics in tight closure theory
by Ananyan, Tigran S., Ph.D., UNIVERSITY OF MICHIGAN, 2009, 71 pages; 3382008

Abstract:

The dissertation adresses some properties of the phantom projective resolutions. The main results are the counterexamples to 15 year old conjectures stated by I. Aberbach in [1]. In the thesis it is shown that a module can have a finite phantom projective dimension locally but not globally, and that a direct summand of a module of finite phantom projective dimension can have itself have no finite phantom projective resolution. Along the way some technique dealing with reducing the phantom resolution to simpler forms is developed. Another important result is a characterization of test elements for tight closure for some wide class of rings R in terms of module-finite extensions of R within R 1/p.

 
AdviserMelvin Hochster
SchoolUNIVERSITY OF MICHIGAN
SourceDAI/B 70-10, p. , Dec 2009
Source TypeDissertation
SubjectsMathematics
Publication Number3382008
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