Motivic Decomposition of Projective Pseudo-Homogeneous Varieties
dc.contributor.advisor | Brosnan, Patrick | en_US |
dc.contributor.author | Srinivasan, Srimathy | en_US |
dc.contributor.department | Mathematics | en_US |
dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
dc.date.accessioned | 2016-09-03T05:42:01Z | |
dc.date.available | 2016-09-03T05:42:01Z | |
dc.date.issued | 2016 | en_US |
dc.description.abstract | Let 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.identifier | https://doi.org/10.13016/M23B82 | |
dc.identifier.uri | http://hdl.handle.net/1903/18597 | |
dc.language.iso | en | en_US |
dc.subject.pqcontrolled | Mathematics | en_US |
dc.subject.pquncontrolled | Characteristic p | en_US |
dc.subject.pquncontrolled | Chow motives | en_US |
dc.subject.pquncontrolled | Linear algebraic groups | en_US |
dc.subject.pquncontrolled | Projective homogeneous varieties | en_US |
dc.subject.pquncontrolled | Pseudo homogeneous variety | en_US |
dc.subject.pquncontrolled | Variety of unseparated flags | en_US |
dc.title | Motivic Decomposition of Projective Pseudo-Homogeneous Varieties | en_US |
dc.type | Dissertation | en_US |
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