Persistent Link:
http://hdl.handle.net/10150/290212
Title:
Crystalline representations and Neron models
Author:
Marshall, Susan Hammond
Issue Date:
2001
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:
We define and study the maximal crystalline subrepresentation functor, Crys(-), defined on p-adic Galois representations of the absolute Galois group of a finite extension K of Q(p) . In particular, we define and study the derived functors, Rⁱ Crys(-), of Crys(-). We then apply these functors to the study of Neron models of abelian varieties defined over K. We extend a formula of Grothendieck expressing the component group of a Neron model in terms of Galois cohomology. The extended formula is only valid for abelian varieties with semistable reduction defined over an unramified base. We explore the failure of the formula in the non-semistable case through the example furnished by Jacobians of Fermat curves.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Kim, Minhyong

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleCrystalline representations and Neron modelsen_US
dc.creatorMarshall, Susan Hammonden_US
dc.contributor.authorMarshall, Susan Hammonden_US
dc.date.issued2001en_US
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.abstractWe define and study the maximal crystalline subrepresentation functor, Crys(-), defined on p-adic Galois representations of the absolute Galois group of a finite extension K of Q(p) . In particular, we define and study the derived functors, Rⁱ Crys(-), of Crys(-). We then apply these functors to the study of Neron models of abelian varieties defined over K. We extend a formula of Grothendieck expressing the component group of a Neron model in terms of Galois cohomology. The extended formula is only valid for abelian varieties with semistable reduction defined over an unramified base. We explore the failure of the formula in the non-semistable case through the example furnished by Jacobians of Fermat curves.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_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.advisorKim, Minhyongen_US
dc.identifier.proquest3016487en_US
dc.identifier.bibrecord.b41936711en_US
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