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A $G$-module is called a tilting module if it has both good and Weyl filtrations.\n  In 1997, it was conjectured by J.E. Humphreys that when $p\\geq h$, the support varieties of the indecomposable tilting modules coincide with the nilpotent orbits given by the Lusztig bijection. 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Hardesty","submitted_at":"2015-07-03T17:17:43Z","abstract_excerpt":"Let $G$ 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. A $G$-module is called a tilting module if it has both good and Weyl filtrations.\n  In 1997, it was conjectured by J.E. Humphreys that when $p\\geq h$, the support varieties of the indecomposable tilting modules coincide with the nilpotent orbits given by the Lusztig bijection. 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