The Frobenius Endomorphism and Multiplicities.

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dc.contributor.author Ma, Linquan en_US
dc.date.accessioned 2014-10-13T18:20:24Z
dc.date.available NO_RESTRICTION en_US
dc.date.available 2014-10-13T18:20:24Z
dc.date.issued 2014 en_US
dc.date.submitted en_US
dc.identifier.uri http://hdl.handle.net/2027.42/108971
dc.description.abstract The dissertation utilizes the Frobenius endomorphism in positive characteristic to attack several problems in local cohomology and multiplicities. The first main result proves that local cohomology modules (supported at the maximal ideal) of an F-pure local ring have only finitely many F-stable submodules. Recent applications of this result such as special cases of the deformation of F-injectivity are discussed. The second main result shows that the category of Lyubeznik's F-modules has finite global dimension one more than the dimension of the ring. In the final part we use Cohen factorization coupled with the Frobenius endomorphism to attack the long standing Lech's conjecture on multiplicities of local rings. We obtain some positive results in low dimension and extend many known results. en_US
dc.language.iso en_US en_US
dc.subject Frobenius, Local Cohomology, F-modules, Multiplicity, Lech's Conjecture en_US
dc.title The Frobenius Endomorphism and Multiplicities. en_US
dc.description.thesisdegreename PhD en_US
dc.description.thesisdegreediscipline Mathematics en_US
dc.description.thesisdegreegrantor University of Michigan, Horace H. Rackham School of Graduate Studies en_US
dc.contributor.committeemember Hochster, Melvin en_US
dc.contributor.committeemember Bass, Hyman en_US
dc.contributor.committeemember Smith, Karen E. en_US
dc.contributor.committeemember Mustata, Mircea en_US
dc.contributor.committeemember Derksen, Harm en_US
dc.subject.hlbsecondlevel Mathematics en_US
dc.subject.hlbtoplevel Science en_US
dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/108971/1/lquanma_1.pdf
dc.owningcollname Dissertations and Theses (Ph.D. and Master's)
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