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dc.contributor.authorHardesty, William Dietrich
dc.date.accessioned2016-10-06T04:30:21Z
dc.date.available2016-10-06T04:30:21Z
dc.date.issued2016-05
dc.identifier.otherhardesty_william_d_201605_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/hardesty_william_d_201605_phd
dc.identifier.urihttp://hdl.handle.net/10724/36129
dc.description.abstractLet $G$ be a reductive algebraic group scheme defined over $mathbb{F}_p$ and let $G_1$ denote the Frobenius kernel of $G$. To each finite-dimensional $G$-module $M$, one can define the support variety $V_{G_1}(M)$, which can be regarded as a $G$-stable closed subvariety of the nilpotent cone. In this thesis we will analyze the support varieties for two types of modules: higher line bundle cohomology groups and tilting modules. In Part 1 we will compute the support varieties of the higher line bundle cohomology groups for $G=SL_3$. A $G$-module is called a tilting module if it has both good and Weyl filtrations. In 1997, it was conjectured by J.E. Humphreys that when $pgeq h$, the support varieties of the indecomposable tilting modules align with the nilpotent orbits given by the Lusztig bijection. Part 2 will be devoted to proving this conjecture when $G=SL_n$ and $p > n+1$.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectRepresentation Theory
dc.subjectAlgebraic Groups
dc.subjectSupport Varieties
dc.subjectTilting Modules
dc.titleOn support varieties for algebraic groups
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorDaniel K. Nakano
dc.description.committeeDaniel K. Nakano
dc.description.committeeDaniel Krashen
dc.description.committeeWilliam Graham
dc.description.committeeLeonard Chastkofsky


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