Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

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dc.contributor.advisorBrosnan, Patricken_US
dc.contributor.authorSrinivasan, Srimathyen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2016-09-03T05:42:01Z
dc.date.available2016-09-03T05:42:01Z
dc.date.issued2016en_US
dc.description.abstractLet G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.en_US
dc.identifierhttps://doi.org/10.13016/M23B82
dc.identifier.urihttp://hdl.handle.net/1903/18597
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledCharacteristic pen_US
dc.subject.pquncontrolledChow motivesen_US
dc.subject.pquncontrolledLinear algebraic groupsen_US
dc.subject.pquncontrolledProjective homogeneous varietiesen_US
dc.subject.pquncontrolledPseudo homogeneous varietyen_US
dc.subject.pquncontrolledVariety of unseparated flagsen_US
dc.titleMotivic Decomposition of Projective Pseudo-Homogeneous Varietiesen_US
dc.typeDissertationen_US

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