Smooth Integral Models for Certain Congruence Subgroups of Odd Spin Groups

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dc.contributor.advisorCunningham, Clifton
dc.contributor.advisorGreenberg, Matthew
dc.contributor.authorShahabi, Majid
dc.contributor.committeememberBauer, Kristine
dc.contributor.committeememberBauer, Mark
dc.contributor.committeememberGour, Gilad
dc.contributor.committeememberGordon, Julia
dc.date2018-11
dc.date.accessioned2018-09-20T14:33:36Z
dc.date.available2018-09-20T14:33:36Z
dc.date.issued2018-09-13
dc.description.abstractIn this thesis, we introduce a family of congruence subgroups for general odd spin groups GSpin(2n+1)/Q (see Chapter 1 for definition of GSpin(2n+1)). We prove that our congruence subgroups for GSpin(2n+1) admit integral models that are smooth group schemes over Z with generic fibre isomorphic to GSpin(2n+1)/Q (Proposition 2.7 and Theorem 2.9), have specific special fibres (Proposition 2.12 and Theorem 2.13), and generalize Hecke's congruence subgroup for GL2(Q) (Proposition 2.15) and the paramodular subgroup for GSp4(Q) (Proposition 2.16), where N is a fixed positive integer. We also study a family of congruence subgroups for special odd orthogonal groups SO(2n+1)/Q, introduced by Gross and Tsai [G2, T1, T2]. These congruence subgroups are expected to appear in anologs of modularity for abelian varieties predicted by the Langlands program [G2,CD]. Using scheme theory, we prove that these congruence subgroups for SO(2n+1) admit integral models that are smooth group schemes over Z[1/2] with generic fibre isomorphic to SO(2n+1)/Q (Theorems 3.6, 3.16, 3.10, 3.17), have specific special fibres (Propositions 3.11 and 3.18, and Theorems 3.12 and 3.19), and have Zp-points isomorphic to the congruence subgroups of SO(2n+1) defined by Gross and Tsai [G2, T1, T2] (Theorems 3.13 and 3.20). We also prove that there exists a close relationship between our integral models for these congruence subgroups of GSpin(2n+1) and SO(2n+1) (Theorem 4.1).en_US
dc.identifier.citationShahabi, M. (2018). Smooth Integral Models for Certain Congruence Subgroups of Odd Spin Groups (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/32950en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/32950
dc.identifier.urihttp://hdl.handle.net/1880/107787
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectSmooth Group Scheme
dc.subjectIntegral Model
dc.subjectCongruence Subgroup
dc.subjectOdd Spin Groups
dc.subject.classificationMathematicsen_US
dc.subject.classificationPhysicsen_US
dc.subject.classificationStatisticsen_US
dc.titleSmooth Integral Models for Certain Congruence Subgroups of Odd Spin Groups
dc.typedoctoral thesis
thesis.degree.disciplineMathematics & Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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