Persistent Link:
http://hdl.handle.net/10150/293444
Title:
Semi-Stable Deformation Rings in Hodge-Tate Weights (0,1,2)
Author:
Park, Chol
Issue Date:
2013
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this dissertation, we study semi-stable representations of G(Q(p)) and their mod p-reductions, which is a part of the problem in which we construct deformation spaces whose characteristic 0 closed points are the semi-stable lifts with Hodge-Tate weights (0, 1, 2) of a fixed absolutely irreducible residual representation ρ : G(Q(p)) → GL₃(F(p)). We first classify the isomorphism classes of semi-stable representations of G(Q(p)) with regular Hodge-Tate weights, by classifying admissible filtered (phi,N)-modules with Hodge-Tate weights (0, r, s) for 0 < r < s. We also construct a Galois stable lattice in some irreducible semi-stable representations with Hodge-Tate weights (0, 1, 2), by constructing strongly divisible modules, which is an analogue of Galois stable lattices on the filtered (ɸ, N)-module side. We compute the reductions mod p of the corresponding Galois representations to the strongly divisible modules we have constructed, by computing Breuil modules, which is, roughly speaking, mod p-reduction of strongly divisible modules. We also determine which Breuil modules corresponds to irreducible mod p representations of G(Q(p)).
Type:
text; Electronic Dissertation
Keywords:
Breuil modules; Deformation rings; Galois representations; Strongly divisible modules; Mathematics; Admissible filtered modules
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Savitt, David

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleSemi-Stable Deformation Rings in Hodge-Tate Weights (0,1,2)en_US
dc.creatorPark, Cholen_US
dc.contributor.authorPark, Cholen_US
dc.date.issued2013-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this dissertation, we study semi-stable representations of G(Q(p)) and their mod p-reductions, which is a part of the problem in which we construct deformation spaces whose characteristic 0 closed points are the semi-stable lifts with Hodge-Tate weights (0, 1, 2) of a fixed absolutely irreducible residual representation ρ : G(Q(p)) → GL₃(F(p)). We first classify the isomorphism classes of semi-stable representations of G(Q(p)) with regular Hodge-Tate weights, by classifying admissible filtered (phi,N)-modules with Hodge-Tate weights (0, r, s) for 0 < r < s. We also construct a Galois stable lattice in some irreducible semi-stable representations with Hodge-Tate weights (0, 1, 2), by constructing strongly divisible modules, which is an analogue of Galois stable lattices on the filtered (ɸ, N)-module side. We compute the reductions mod p of the corresponding Galois representations to the strongly divisible modules we have constructed, by computing Breuil modules, which is, roughly speaking, mod p-reduction of strongly divisible modules. We also determine which Breuil modules corresponds to irreducible mod p representations of G(Q(p)).en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectBreuil modulesen_US
dc.subjectDeformation ringsen_US
dc.subjectGalois representationsen_US
dc.subjectStrongly divisible modulesen_US
dc.subjectMathematicsen_US
dc.subjectAdmissible filtered modulesen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSavitt, Daviden_US
dc.contributor.committeememberCais, Brydenen_US
dc.contributor.committeememberSharifi, Romyaren_US
dc.contributor.committeememberThakur, Dineshen_US
dc.contributor.committeememberSavitt, Daviden_US
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