Reductive and unipotent actions of affine groups
| Autor: | Walter, Ferrer-Santos, Alvaro, Rittatore |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | We present a generalized version of classical geometric invariant theory \`a la Mumford where we consider an affine algebraic group $G$ acting on a specific affine algebraic variety $X$. We define the notions of linearly reductive and of unipotent action in terms of the $G$ fixed point functor in the category of $(G,\Bbbk [X])$--modules. In the case that $X=\{\star\}$ we recuperate the concept of lineraly reductive and of unipotent group. We prove in our "relative" context some of the classical results of GIT such as: existence of quotients, finite generation of invariants, Kostant--Rosenlicht's theorem and Matsushima's criterion. We also present a partial description of the geometry of such linearly reductive actions. Comment: 17 pages |
| Databáze: | arXiv |
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