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dc.contributor.advisorKisin, Mark
dc.contributor.authorWang Erickson, Carl William
dc.date.accessioned2013-09-25T16:59:31Z
dc.date.issued2013-09-25
dc.date.submitted2013
dc.identifier.citationWang Erickson, Carl William. 2013. Moduli of Galois Representations. Doctoral dissertation, Harvard University.en_US
dc.identifier.otherhttp://dissertations.umi.com/gsas.harvard:10933en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:11108709
dc.description.abstractThe theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The central object of study is the geometry of the map \(\bar{\psi}\) from the moduli stack of representations to the moduli scheme of pseudorepresentations. The first chapter culminates in showing that \(\bar{\psi}\) is very close to an adequate moduli space of Alper. In particular, \(\bar{\psi}\) is universally closed. The second chapter refines the results of the first chapter. In particular, certain projective subschemes of the fibers of \(\bar{\psi}\) are identified, generalizing a suggestion of Kisin. The third chapter applies the results of the first two chapters to moduli groupoids of continuous representations and pseudorepresentations of profinite algebras. In this context, the moduli formal scheme of pseudorepresentations is semi-local, with each component Spf \(B_\bar{D}\) being the moduli of deformations of a given finite field-valued pseudorepresentation \(\bar{D}\). Under a finiteness condition, it is shown that \(\bar{\psi}\) is not only formally finite type over Spf \(B_\bar{D}\), but arises as the completion of a finite type algebraic stack over Spec \(B_\bar{D}\). Finally, the fourth chapter extends Kisin's construction of loci of coefficient spaces for p-adic local Galois representations cut out by conditions from p-adic Hodge theory. The result is extended from the case that the coefficient ring is a complete Noetherian local ring to the more general case that the coefficient space is a Noetherian formal scheme.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dash.licenseLAA
dc.subjectMathematicsen_US
dc.subjectGalois representationen_US
dc.subjectmodulien_US
dc.subjectp-adic Hodge theoryen_US
dc.subjectpseudorepresentationen_US
dc.titleModuli of Galois Representationsen_US
dc.typeThesis or Dissertationen_US
dash.depositing.authorWang Erickson, Carl William
dc.date.available2013-09-25T16:59:31Z
thesis.degree.date2013en_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorHarvard Universityen_US
thesis.degree.leveldoctoralen_US
thesis.degree.namePh.D.en_US
dc.contributor.committeeMemberGross, Benedicten_US
dc.contributor.committeeMemberMazur, Barryen_US
dash.contributor.affiliatedWang Erickson, Carl William


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