Cohomology for Frobenius kernels of $SL_2$
| Autor: | Ngo, Nham V. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Journal of Algebra, 396 (2013), 39-60 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2013.07.033 |
| Popis: | Let $(SL_2)_r$ be the $r$-th Frobenius kernels of the group scheme $SL_2$ defined over an algebraically field of characteristic $p>2$. In this paper we give for $r\ge 1$ a complete description of the cohomology groups for $(SL_2)_r$. We also prove that the reduced cohomology ring $\opH^\bullet((SL_2)_r,k)_{\red}$ is Cohen-Macaulay. Geometrically, we show for each $r\ge 1$ that the maximal ideal spectrum of the cohomology ring for $(SL_2)_r$ is homeomorphic to the fiber product $G\times_B\fraku^r$. Finally, we adapt our calculations to obtain analogous results for the cohomology of higher Frobenius-Luzstig kernels of quantized enveloping algebras of type $SL_2$. Comment: published version; a section for the case p=2 is added |
| Databáze: | arXiv |
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